KYIV — NATO said on Monday that some member countries were putting their forces on standby and sending additional ships and fighter jets to Eastern Europe to reassure allies in the region, as Britain joined the United States in ordering families of diplomats out of Ukraine, citing “the growing threat from Russia.”

The moves signaled rising fears of a potential Russian military intervention in Ukraine, as well as increasing concerns about the Kremlin flexing its muscles further afield. Russian troops and equipment are pouring into neighboring Belarus for planned exercises next month that U.S. officials fear are not only directed at Ukraine, but also intended to intimidate NATO countries on Belarus’s western border like Poland and the Baltic countries.

U.S. intelligence officials have said they do not believe President Vladimir V. Putin has made a decision to invade Ukraine, and Russian diplomats have repeatedly said there are no plans to do so.

But with a month’s negotiations between Moscow and Washington at an apparent impasse, Russia and the West increasingly seem to be talking past one another. Even as the White House prepares written responses to Russia’s demands on limiting NATO’s footprint in Europe, the Biden Administration is considering deploying several thousand U.S. troops, as well as warships and aircraft, to NATO allies in the Baltics and Eastern Europe.

On Monday, both NATO and Russia blamed each other for inflaming tensions.

“This all leads to tensions rising,” the Kremlin’s spokesman, Dmitri S. Peskov, said in reference to NATO’s announcement about strengthening its eastern flank. “This is not happening because of what we, Russia, are doing. This is all happening because of what NATO and the United States are doing, and as a result of the information that they are distributing.”

Jens Stoltenberg, the NATO secretary-general, said in a statement Monday that NATO would “continue to take all necessary measures to protect and defend all Allies, including by reinforcing the eastern part of the Alliance.” The statement added: “We will always respond to any deterioration of our security environment, including through strengthening our collective defense.”

The NATO announcement about sending troops and equipment on Monday consolidated statements that member states have made over the last several days. They include an offer by France to send troops to Romania under NATO command; Denmark sending F-16 jets to Lithuania; the Netherlands sending two F-35 jets to Bulgaria to help with air policing, and Spain sending a frigate to the Black Sea.

NATO members bordering Russia and Belarus or near the contested Black Sea in the south have asked for more allied troops and equipment to enhance deterrence against a more aggressive Russia. That would be in addition to the 5,000 or so NATO troops already stationed in Poland and the three Baltic nations that were put there as “enhanced forward presence,” in NATO speak, after the annexation of Crimea in 2014.

There was no indication in NATO’s statement that any additional forces deployed in Central, Eastern or Southern Europe would be used to support Ukraine, which is not a NATO member, in the event of a Russian invasion. Western officials have made clear that NATO forces would not engage militarily against Russia, and the Biden administration has said that goes for the United States as well.

The mobilization by the West comes in response to what Western countries say is a buildup of Russian forces larger than any seen since the end of the Cold War. Ukraine’s military intelligence service calculates that 127,000 troops are amassed on the Ukrainian border and thousands more are expected to pour into Belarus for next month’s exercises, along with tanks, artillery and fighter planes.

But the buildup near Ukraine is only one part of what increasingly appears to be a global activation of Russian forces.

Last week, Russian defense ministry announced that more than 140 ships and 10,000 sailors would take part in a series of live-fire naval exercises in February across the world, including in the Irish coast. The goal, according to the ministry, is to “protect Russia’s national interests in the world’s oceans.”

On Monday, the government of Ireland said it had raised concerns with Moscow about its plans to carry out naval exercises off the Irish coast next month.

Even as NATO countries were stepping up their readiness, the Ukrainian government attempted to project a business-as-usual image. It criticized the United States’ decision to order family members of the U.S. embassy staff to leave Ukraine, calling it “premature” and the result of “excessive caution.”

But other countries were also exercising caution in Kyiv, the Ukraine capital. Britain said that it, too, would withdraw family members of diplomats, and there were reports that Germany and Australia were working to draw down their embassies.

In Kyiv, officials pushed back on the idea that events were so dire that it required Western nations to remove the families of embassy personnel.

“A serious change in the security situation of late has not occurred,” Oleg Nikolenko, the spokesman for Ukraine’s foreign ministry, said in a statement. “The threat of a new wave of Russian aggression has been permanent since 2014, and the build up of Russian forces on the state border began in April last year.”

While the United States has warned that President Vladimir V. Putin of Russia could order an attack at any time, Ukraine’s government has shown less sense of urgency and has at times presented contradictory assessments of the situation. In an address to the nation last week, Ukraine’s president, Volodymyr Zelensky, played down the threat, urging Ukrainians to remain calm and not “run out for buckwheat and matches.”

“This danger has existed for more than one day and it has it has not become greater,” he said.

In his statement, Mr. Nilolenko, the foreign ministry spokesman, suggested that giving into panic would simply give the Russians a victory as it attempts to sow discord through information warfare.

“The Russian Federation is currently working actively to destabilize the internal situation in Ukraine,” he said. “In this situation it is important to soberly evaluate the risks and preserve calm.”

Despite the pullout of family members and some personnel, both the American and British embassies have been ordered to remain open. The State Department said that the decision was made “out of an abundance of caution,” but that the United States would “not be in a position” to evacuate U.S. citizens should Russia invade Ukraine.

European Union foreign ministers are meeting on Monday in Brussels to discuss Ukraine and work more on a coordinated position should Russia further invade. There were no plans as of yet to pull out any European diplomats or their families, said Josep Borrell Fontelles, the bloc’s foreign-policy chief. The European Union also announced further financial aid to Ukraine of some 1.2 billion euros, or $1.36 billion, to help the country during this crisis.

Michael Schwirtz reported from Kyiv and Steven Erlanger from Brussels. Anton Troianovski contributed reporting from Moscow.