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And Prime Minister Viktor Orban of Hungary continues to block even a watered-down European Union effort to put an embargo on Russian oil, part of a sixth package of sanctions aimed at Moscow.

While NATO and the European Union have shown remarkable unity in their response to Mr. Putin’s war, the actions of both authoritarian leaders show the strains building as the war drags on, peace talks appear to go nowhere, and Western sanctions are causing economic pain and high inflation at home, as well as in Russia.

Mr. Erdogan and Mr. Orban may be outliers in their organizations, but they are able to use the requirement for consensus in both NATO and the E.U. to get their political concerns addressed by blocking unified action, even temporarily.

On Wednesday, a meeting of NATO ambassadors could not reach consensus on a first vote to proceed with the requests for membership because Turkey said it first wanted NATO to address its security concerns. In particular, Ankara wants Finland and especially Sweden to end what Mr. Erdogan has called support for “terrorist organizations” in their countries, primarily the Kurdistan Workers’ Party, or PKK, as well as to lift export bans on certain arms sales to Turkey.

Turkey’s decision to block consensus came hours before the Turkish foreign minister, Mevlut Cavusoglu, was set to meet with Secretary of State Antony J. Blinken in New York; Turkey wants its security concerns to be addressed before NATO’s annual summit meeting in late June.

In an address to his lawmakers in Parliament on Wednesday, Mr. Erdogan criticized at length Western support for Kurdish groups that Ankara sees as a terrorist threat. But he has not said that he would veto Finland and Sweden’s applications.

The PKK is a Kurdish guerrilla group that has fought a decades-long separatist insurgency in parts of Turkey. It was designated by the United States as a terrorist organization in 1997.

National security is Mr. Orban’s argument, too. Hungary is dependent on Russia for its energy, getting 85 percent of its natural gas and 65 percent of its oil supply from Russia, as well as using Russian technology for its nuclear power plants.

While Hungary has approved all previous sanction packages, including an embargo on Russian coal, Mr. Orban proclaimed that an oil embargo would be the equivalent of an “atomic bomb” for the Hungarian economy.

But like Mr. Erdogan in NATO, Mr. Orban this time is the sole holdout, in his case, in the weekslong E.U. efforts to finalize a gradual embargo.

Talks began in mid-April. After extensive consultation between E.U. officials and diplomats from the bloc’s 27 member states, a proposal was put on the table in early May.

But Hungary seemed to be moving the goal posts. The first proposal gave extensions to Hungary and Slovakia so they could find alternative suppliers. While the other 25 E.U. members would have until the end of the year, Hungary and Slovakia would have until the end of 2023.

Then Hungary demanded, and secured, even more time. The latest version of the package would grant it until the end of 2024, but Mr. Orban has insisted that Hungary would need billions from the bloc to shield his nation’s economy.

Diplomats said that they expected Mr. Orban eventually to acquiesce to an oil embargo, having secured both a long extension and extra funding for Hungary, but that he could drag the talks out even longer, perhaps until the end of the month when leaders are set to meet in person in Brussels.

NATO officials expressed the same confidence about Mr. Erdogan — that he will eventually agree to back Sweden and Finland joining NATO in return for some concessions that will help him politically at home, with his economy in crisis and new elections only a year away.

Alexander Stubb, a former Finnish prime minister and foreign minister, said that “the Finns are cool and collected and so are the Swedes — this will work out.”