Roughly 5,000 doses of monkeypox vaccine intended for Fort Lauderdale, Fla., left the national stockpile’s warehouse in Olive Branch, Miss., on July 19. They somehow ended up in Oklahoma.

Then Tennessee. Then Mississippi again. Then, finally, Florida.

In Idaho, a shipment of 60 vaccine doses disappeared and showed up six days later, refrigerated rather than frozen, as needed. Another 800 doses sent to Minnesota — a significant portion of the state’s total allotment — were unusable because the shipment was lost in transit for longer than the 96-hour “viability window.”

The federal government’s distribution of monkeypox vaccine has been blemished by missteps and confusion, burdening local officials and slowing the pace of immunizations even as the virus spreads, according to interviews with state health officials and documents obtained by The New York Times.

Officials in at least 20 states and jurisdictions have complained about the delivery of the vaccine, called Jynneos. (More than half are led by Democrats, including California, Washington, Connecticut and Michigan, suggesting that their grievances are not politically motivated.)

“This is happening everywhere,” said Claire Hannan, executive director of the Association of Immunization Managers, a nonprofit group that represents state, local and territorial officials.

“Our response is completely inefficient and breaking the back of state and local responders,” she added. Ms. Hannan said she had never “seen this level of frustration and stress.”

In previous emergencies, including the 2009 swine flu outbreak and the Covid-19 pandemic, vaccines were delivered directly from manufacturers to health care providers through a system run by the Centers for Disease Control and Prevention.

That system, called VTrckS (pronounced “vee-tracks”), routinely moves billions of vaccine doses for annual immunizations and, importantly, is integrated with state databases that track vaccinations and doses.

But Jynneos is being disbursed from the National Strategic Stockpile by a different government agency under the Department of Health and Human Services. That agency was never set up to take ongoing orders, arrange deliveries from the stockpile, track shipments or integrate with state systems.

Instead, the stockpile was designed to deliver massive amounts of vaccine to each state in response to a catastrophic event, according to a federal official with knowledge of the stockpile’s operations.

“If it was a smallpox response, they’re not going to be sitting in their offices ordering vaccine,” the official said of state health authorities. The stockpile is intended to be “pushing products out — it’s not an ordering-based system,” the official added.

As it stands now, the stockpile is shipping monkeypox vaccine to just five sites in each state, regardless of its size. State officials must distribute the doses, track them manually and enter the data into their databases, none of which would have been necessary under the C.D.C.’s system.

Until recently, orders for Jynneos had to be placed via email instead of an automated system, and state officials often did not know where their deliveries were or whether they had been sent at all.

Some containers arrived without labels saying they contained vaccines or needed cold storage. Some were tracked down only after multiple emails and phone calls. Doses of Jynneos have arrived in the dead of night.

“We had no way to track vaccine shipments, when they actually shipped or when they were going to arrive,” Chris Van Deusen, director of media relations at the Texas Department of State Health Services, said in an email. “They just showed up with no notice.”

H.H.S. officials two weeks ago switched to a different ordering system, which has been used to deliver antiviral drugs from the stockpile. But that system is also not linked to state immunization databases, and it is not well suited to monitoring the special conditions needed for transporting vaccines, several state officials said in interviews.

In a statement, the H.H.S. said that of more than 1,100 deliveries of Jynneos, “only a minuscule number of shipments have experienced issues.” The stockpile “has not experienced any loss of Jynneos vaccine in transit for any reason, including temperature excursions,” the statement said.

The delivery flaws threaten to aggravate tensions between federal health officials and their state counterparts. Xavier Becerra, the H.H.S. secretary, recently suggested that states and localities should be doing more to help contain the monkeypox outbreak.

But allegations that states are not requesting all their available vaccine doses or are shirking their responsibilities don’t tell the whole story, some officials said.

“We don’t want to point fingers at any of our partners on any level of government,” said Dr. Umair Shah, secretary of health for Washington State. But “the system that the federal government put in place was, in essence, clunky.”

The traditional system for delivering vaccines, VTrckS, has been operated for years by McKesson, a drug and medical supply distributor, under contract with the C.D.C.

VTrckS processes orders, tracks shipments, offers delivery estimates and notifications, and is integrated with state registries so that each package of vaccines can be tracked and easily redistributed from one provider to another when necessary.

In the past, “we have literally done nothing except basically hit an approve button,” said Kathryn Turner, the deputy state epidemiologist of Idaho and secretary and treasurer for the Council of State and Territorial Epidemiologists. “It’s a very slick system, and it’s worked for years and years and years.”

Other state officials said they were baffled by the decision to use a new ordering process that required emailing and manual data entry during a rapidly escalating outbreak.

“We have the systems in place,” said Jeremy Redfern, a spokesman for the Florida Department of Health. “Why they’re not using them, I don’t really know.”

H.H.S. considered several options for delivering the vaccine from the national stockpile, but other systems “could not be implemented on the timeline needed for distribution of Jynneos,” the department said in its statement.

It would take several months to integrate VTrckS with the stockpile, the statement said. The department is seeking a commercial partner to improve delivery.

As of Thursday, the United States recorded nearly 11,000 monkeypox cases, although the real number is thought to be much higher.

Federal officials have allocated 1.1 million doses of Jynneos to states and have said they shipped about 600,000 of those. Even when all the doses are distributed, the nation will be a long way from the roughly three million shots needed to protect men who have sex with men, who have been most at risk in the current outbreak. (Federal health officials are considering stretching the supply by giving the shots in a different way.)

State officials are permitted to order only 40 percent of the remaining doses immediately and another 30 percent on Monday. “When and whether” the final 30 percent will be available is yet to be determined, Mr. Van Deusen, the Texas official, said.

Mr. Van Deusen said that the pace of distribution slowed significantly throughout July, with shipments arriving more than a week after they were ordered.

Some states are struggling with distribution even after shipments from the stockpile have arrived.

State officials must determine when and how to roll out doses from their five allotted sites and must manually track them. It is a painstaking process, particularly in large states, for which most health departments have neither the staff nor the funding to hire new workers.

States are wrestling with whether to roll them out immediately or hold some back for unexpected situations, and whether to store the doses centrally or send them to localities so they are ready to go. Federal officials have not provided much guidance, as they did when distributing Covid vaccines.

Big states in particular have found it challenging to move Jynneos from five receiving sites to local hubs and from there to individual providers. The loading and unloading at each step require time and labor, and jeopardize the cold storage and careful handling needed.

Public health departments have been underfunded and overworked for years, and the Covid-19 pandemic has made the problems worse. Many jurisdictions simply don’t have the capacity to deal with a new outbreak.

“There’s just all of these parts of the system that are stressed, are really strained,” said Dr. Anne Zink, Alaska’s chief medical officer and the president-elect of the Association of State and Territorial Health Officials. “It’s no wonder people are frustrated on all levels.”

Some state officials said they resented the suggestion by the federal government that they were slowing the country’s response by withholding monkeypox data from federal agencies.

Many officials are prevented by state laws from sharing data on cases and vaccinations, and even states that can send information now have to enter it manually into the ordering system and their own databases.

State officials have “had terse discussions” about these issues with H.H.S. officials, said Dr. Christine Hahn, medical director for the Idaho Division of Public Health.

“Instead of you and C.D.C. talking and sharing data,” Dr. Hahn said state officials told the agency, “you throw new systems at us and then say, ‘Boy, the states aren’t sharing the data.’”

Not all states say they have experienced vaccine distribution problems. Officials in New York said that vaccines ordered within the last week had arrived as scheduled, but declined to elaborate on deliveries before then.

In an email to The Times, California’s health department said: “To date, there have been no issues with ordering and receipt of the monkeypox medical countermeasures.”

But in calls with federal agencies and with the Association of Immunization Managers, health officials in California, Pennsylvania, Wisconsin, Michigan, Minnesota, Connecticut, Illinois and Indiana have all voiced frustration with federal handling of the vaccine.

“Everyone expressed frustration” that VTrckS was not given more consideration, read the notes from a call between state and federal officials on July 20, and they “made it clear that all states would rather go that route A.S.A.P.”

H.H.S.’s new solution — the ordering system introduced last week — is still far from ideal, some state officials said. “The processes for monkeypox and Covid-19, then, have states using multiple systems,” said Ken Gordon, a spokesman for Ohio’s department of health. “It has been challenging.”

Management of the national stockpile switched hands in 2018 from the C.D.C. to a different federal agency within the H.H.S. But state officials said that they had no idea that vaccine delivery from the national stockpile would also be changing, and that the C.D.C.’s system would no longer be used.

“That might be the right decision long-term, but boy, short-term for us, it’s definitely caused some hiccups,” Dr. Hahn said.

H.H.S. staff began training state workers to use the new system put in place two weeks ago in a webinar four days before it was deployed.

The H.H.S. said that as of Aug. 8, more than 99 percent of the vaccines had been ordered and all state health departments had received their doses. Still, some states were reporting difficulties getting their doses.

The new program may “grow into something later that’s better and is actually functional,” Dr. Zink said. But “it’s definitely not there now.”