Administration officials intend the prospect of the sale to prod Turkey to sign off on Finland and Sweden’s accession to the North Atlantic Treaty Organization, which Ankara has blocked over objections to their ties to Kurdish separatist groups. Congress’s approval of the sale is contingent on Turkey’s acquiescence, administration officials said. The two countries ended decades of neutrality when they decided to join NATO last year in reaction to Russia’s invasion of Ukraine.

The sale to Turkey, which the administration has been considering for more than a year, is larger than expected. It includes 40 new aircraft and kits to overhaul 79 of Turkey’s existing F-16 fleet, according to officials familiar with the proposals.

Congressional notification of the deal will roughly coincide with a visit to Washington next week by Turkey’s Foreign Minister

Mevlut Cavusoglu.

The sale to Turkey also includes more than 900 air-to-air missiles and 800 bombs, one of the officials said.

The separate sale to Greece, which was requested by the Greek government in June 2022, includes at least 30 new F-35s. The F-35 Joint Strike Fighter is the U.S.’s most advanced jet fighter. While officials described the timing of the notifications for both Turkey and Greece as coincidental, it could quell protests from Athens over the F-16 sale if its request is also granted. Greece and Turkey are historic regional rivals and a sale to Turkey alone would likely draw swift condemnation from Athens.

The potential sale of the aircraft could have far-reaching implications for Washington’s efforts to shore up ties with a pair of NATO allies amid the Western response to Russia’s assault on Ukraine.

A State Department spokesman declined to comment on potential arms transfers as a matter of policy until and unless they are formally notified to Congress. Congress has never successfully blocked a foreign arms sale requested by the White House.

The proposed deal with Turkey comes at a moment of tension in U.S.-Turkish relations, with Washington also attempting to convince President Recep

Tayyip Erdogan

to do more to enforce sanctions on Russia and to approve the entry of Finland and Sweden into NATO.

The proposal also sets up a possible showdown with some congressional leaders who have vowed to oppose weapons sales to Turkey. Sen.

Bob Menendez,

a Democrat from New Jersey who is the chairman of the Senate Foreign Relations Committee, has said he wouldn’t approve any F-16 sale to Turkey, citing human-rights concerns.

In recent months, Mr. Erdogan has also threatened to launch a new military incursion against Kurdish militants in Syria. Last month a Turkish court also convicted the mayor of Istanbul, a popular opponent of Mr. Erdogan, of insulting public officials in what human rights groups said was part of a crackdown on the Turkish opposition. The Turkish government says its courts are independent.

Under U.S. arms-export laws, Congress will have 30 days to review the deal. If Congress wants to block the deal it must pass a joint resolution of disapproval. Congress can also pass legislation to block or modify a sale at any time until the delivery.

U.S. officials say they are encouraging Mr. Erdogan to drop his opposition to Finland and Sweden joining NATO. One official characterized the F-16s as the “carrot on a stick” to get Turkey to agree.

This, officials said, could ease opposition to the sale among some members of Congress. Officials within the State Department have argued for months that the expansion was imperative to NATO’s collective security. However, officials expect that while the Greece package could sail through Congress, the F-16s may be delayed over some members’ reluctance to embolden Ankara with the additional firepower.

Mr. Erdogan first threatened to veto the two countries’ entrance over their ties to Kurdish militant groups in Iraq and Syria. Turkey has fought a slow-burning war with Kurdish armed groups for decades in a conflict that has left tens of thousands dead.

NATO leaders say that Finland and Sweden have addressed Turkey’s concerns, upholding an agreement signed last year that called for both countries to evaluate Turkish extradition requests and drop restrictions on arms sales to Ankara.

Turkish officials say that Sweden hasn’t done enough to uphold its obligations to Turkey, citing what they say is continuing activity by the militant Kurdistan Workers’ Party in Sweden. The Turkish government this week summoned Sweden’s ambassador over a demonstration in Stockholm in which protesters hung a puppet of Mr. Erdogan by its feet. The Turkish president’s hard line against Sweden has broad support within Turkey, including among opposition parties, who have long opposed what they see as a permissive approach to Kurdish militant groups in Europe.

The timing of a vote on NATO expansion in the Turkish parliament will also depend on Turkey’s national election this year, in which Mr. Erdogan faces a close race amid public discontent over the country’s struggling economy.

The Turkish Ministry of Foreign Affairs didn’t respond to a request for comment.

The Biden administration remains cautiously optimistic that Turkey will eventually come around on Finland and Sweden. U.S. officials said last year that there would be no quid pro quo for Turkey’s approval of the NATO expansion, and said that the timing of the F-16 sale was dependent on the administration’s own internal process to complete the deal.

The proposed sales also come amid heightened tensions between Turkey and Greece, two longtime adversaries who have traded threats over the past year in the eastern Mediterranean.

Turkey was originally a participant in the U.S.’s cutting-edge F-35 program but was expelled after Mr. Erdogan approved the purchase of Russia’s S-400 air defense system. The U.S. government said the Russian weapons system could potentially hack the F-35.

Biden administration officials have argued that selling F-16s to Turkey could help restore ties with the country, which maintains the second-largest army in NATO.

Under Mr. Erdogan, Turkey has played an important role in the Ukraine crisis, facilitating negotiations over prisoner exchanges and helping to broker an agreement that allowed Ukraine to resume its exports of grain through Black Sea ports. Mr. Erdogan’s close relationship with Russia’s President

Vladimir Putin

has also raised concerns in Washington, with scrutiny of inflows of Russian money to Turkey, including oligarch assets.

—William Mauldin contributed to this article.

Write to Jared Malsin at jared.malsin@wsj.com and Vivian Salama at vivian.salama@wsj.com