President Vladimir V. Putin’s disdain for his Ukrainian counterpart runs so deep that he almost never utters the name “Zelensky.” The Kremlin insists he’s an illegitimate leader. Russian state television calls him a “clown.”

But President Trump has pinned his recent flurry of diplomacy on the idea that Mr. Putin and President Volodymyr Zelensky will have to come face to face in order to end Russia’s war. Mr. Trump said he “began the arrangements” for such a meeting when he spoke by phone with Mr. Putin on Monday.

And so the whirlwind of diplomatic intrigue in Moscow amid Mr. Trump’s push to halt the fighting shifted to a new mystery on Tuesday: Could the war’s central archenemies soon sit down one on one?

For Mr. Putin, such a summit could be a way to cement a peace deal that the Kremlin would cast as a victory, if Mr. Trump were to pressure Mr. Zelensky to accept Mr. Putin’s demands on Ukraine’s land and sovereignty. But it could also carry political risks, since the Kremlin has long signaled that negotiating directly with Mr. Zelensky would be beneath the Russian leader.

“It would be a compromise,” Konstantin Zatulin, a senior Russian lawmaker, said in a phone interview on Tuesday, casting a potential Putin-Zelensky meeting as a Kremlin concession in itself. “Russia would withdraw its concerns about a meeting with Zelensky in order to support President Trump’s peacemaking efforts.”

Mr. Zatulin said some Russian officials believed Mr. Putin should not meet with Mr. Zelensky in any scenario, given that “Russia has been talking everywhere about Zelensky’s illegitimacy.” But Mr. Zatulin said that in his view, a summit with Mr. Zelensky should be considered because “the stakes are just too high to keep ignoring any possibility of a meeting.”

The Kremlin, as always, has tried to keep its options open, continuing to telegraph this week that a Putin-Zelensky meeting was possible but offering no indication that it was imminent. Analysts who study the Kremlin said it was hard to imagine Mr. Putin agreeing to a meeting unless it was clear that Mr. Zelensky was prepared to accede to Russia’s key demands.

“I simply don’t see any prospect of such a meeting being organized in the near future or even in the foreseeable future,” Grigorii Golosov, a political scientist in St. Petersburg, Russia, said in a phone interview. He predicted that Mr. Putin would meet with Mr. Zelensky only “if it becomes clear to Putin that this meeting is needed for Ukraine to capitulate, for Zelensky to admit his defeat.”

To sit down with Mr. Zelensky for a purpose short of that could stir controversy in Russia. Mr. Putin has staked the narrative of his invasion on the false idea that Mr. Zelensky leads a “regime” guilty of genocide against Russian speakers. Mr. Zelensky himself grew up speaking Russian and initially stirred hopes in Moscow of a more Russia-friendly Ukrainian government when he was elected president in a landslide in 2019.

Mr. Putin has since spoken of Mr. Zelensky in venomous terms. In 2023, for example, Mr. Putin attacked Mr. Zelensky’s Jewish identity. Mr. Putin said his Jewish friends had told him that “Zelensky isn’t Jewish — he’s a disgrace to the Jewish people.”

A one-on-one negotiation could allow Mr. Putin and Mr. Zelensky to be seen as equals. That is why Mr. Trump’s insistence that a meeting between Mr. Zelensky and Mr. Putin is in the works has stretched belief for many.

“Maybe they are getting along a little bit better than I thought,” Mr. Trump said of the Ukrainian and Russian leaders in a Fox News interview on Tuesday. While there is no evidence of any rapport between Mr. Putin and Mr. Zelensky, Mr. Trump said it was the reason he had proposed that the two men meet first one on one, rather than in a three-way format with Mr. Trump.

“Otherwise I wouldn’t have set up the two meeting, I would have set up the three, the trilat,” Mr. Trump said.

Mr. Trump said he had told Mr. Putin that he would set up a two-way meeting between Mr. Zelensky and Mr. Putin in their phone call on Monday, just after Mr. Trump met with Mr. Zelensky and European leaders at the White House. Mr. Zelensky told reporters, as he has in the past, that he was ready to meet with Mr. Putin.

But when Mr. Putin’s foreign policy adviser Yuri Ushakov summarized the phone call for reporters, he made no mention of an upcoming summit.

Mr. Trump and Mr. Putin discussed “exploring opportunities to bring more senior officials” into direct talks between Russia and Ukraine, Mr. Ushakov said, without specifying who those officials would be.

Sergey V. Lavrov, Russia’s foreign minister, was similarly vague in a state television interview on Tuesday. He said that while the Kremlin was not against a bilateral meeting between Mr. Zelensky and Mr. Putin in principle, “any contacts involving top officials should be prepared very carefully.”

Analysts have noted an unusual burst of diplomatic activity by Mr. Putin that suggests he is taking Mr. Trump’s push seriously. The Kremlin said that Mr. Putin had called the leaders of Saudi Arabia, Kyrgyzstan, Brazil, India, Tajikistan, South Africa, Uzbekistan, Kazakhstan and Belarus this week to update those governments on developments in Ukraine talks.

Mr. Putin “appears to have decided that the time for real diplomacy has come,” said Dmitri Trenin, a specialist on security policy at the Higher School of Economics in Moscow. “The contours of the solution that Putin has probably discussed with Trump suit him.”

Mr. Trenin predicted that Mr. Putin would agree to a meeting with Mr. Zelensky if the Kremlin was satisfied with the concessions that the Ukrainian president would be willing to make. But he added that Mr. Putin’s far-reaching demands remained on the table, including not only his claims on Ukrainian territory but also his insistence that Ukraine limit the future size of its military.

Looming over the possibility of a Putin-Zelensky meeting was Mr. Trump, who appears to have pushed Mr. Putin to become more willing to engage with Mr. Zelensky, analysts said. In February, Mr. Putin angered Mr. Trump by suggesting that the war may end only if the Zelensky government is replaced by a temporary administration installed under the auspices of the United Nations.

“Russia’s rhetoric has softened since then,” Mr. Golosov, the St. Petersburg political scientist, said. “There’s still plenty of abuse directed at Zelensky, but they don’t dare say anymore that he is such an illegitimate president that there is no need to talk to him.”

Mr. Zatulin, the Russian lawmaker, said that the Kremlin’s consideration of a meeting with Mr. Zelensky was part of Russia’s effort “to demonstrate that it’s prepared to come to agreements with Trump.”

“Russia has chosen this path, and it’s had an influence on Trump,” he said.

There was little discussion of the possibility of a Putin-Zelensky meeting on Russian state television on Tuesday, while the Kremlin-directed networks’ ridicule of Mr. Zelensky continued apace. Olga Skabeyeva, a host on the political talk show “60 Minutes,” said Mr. Zelensky had acted “like a schoolboy” during his White House visit on Monday, laughing “stupidly” and speaking “as always in his clumsy English.”

But analysts predicted that should Mr. Putin decide it advantageous to hold such a summit, the propaganda message could turn on a dime. As a result, there was little concern in the Kremlin that a meeting with Mr. Zelensky would carry a heavy political cost for Mr. Putin, said Mikhail Vinogradov, a Moscow political analyst.

“The propaganda apparatus assumes that society is ready to accept any result of negotiations and military actions,” Mr. Vinogradov said. “Society is not a big limiting factor here. It has already gotten used to many things.”

Alina Lobzina contributed reporting from London, and Ivan Nechepurenko from Moscow.