The Kremlin on Sunday hailed the dialogue between Russian President Vladimir Putin and his US counterpart Donald Trump as "promising", while Ukraine's leader offered to step down in exchange for NATO membership.

Trump broke with Western policy earlier this month by phoning Putin to discuss how to end the Russia-Ukraine conflict — a call hailed by Moscow as ending three years of isolation for Putin since he launched the special military operation in February 2022.

Top Russian and United States officials met in Riyadh, Saudi Arabia, last week to discuss the "restoration" of ties and start a discussion on a possible Ukraine cease-fire — all without the involvement of Kyiv or Europe.

"This is a dialogue between two extraordinary presidents," Kremlin spokesman Dmitry Peskov told state TV, adding "that's promising".

"It is important that nothing prevents us from realizing the political will of the two heads of state," he said.

Peskov ruled out any territorial concessions as part of a settlement. "The people decided to join Russia a long time ago," he said, referring to Moscow-staged votes in eastern Ukraine held amid the special military operation, which were slammed as bogus by Kyiv, the West and some international monitors.

"No one will ever sell off these territories. That's the most important thing," Peskov said.

Amid his outreach to Moscow, Trump has also verbally attacked Ukrainian President Volodymyr Zelensky, claiming Kyiv started the conflict and that Zelensky was hugely unpopular at home.

Zelensky said on Sunday he was not "offended" by Trump's comments and was ready to test his popularity in elections once martial law ends in Ukraine.

"One would be offended by the word 'dictator' if he was a dictator," Zelensky said.

He also called for the Western coalition that has been helping Kyiv during the conflict for the past three years to hold strong.

"We must do our best to achieve a lasting and just peace for Ukraine. This is possible with the unity of all partners: we need the strength of the whole of Europe, the strength of America, the strength of all those who want lasting peace," he said.

Conditional resignation

During a news conference in Kyiv on Sunday, Zelensky said he was ready to quit as president if it meant Ukraine would be admitted to the NATO military alliance.

He spoke as Russia's TASS news agency reported that US and Russian diplomats would meet in the coming week, a follow-up to the Riyadh talks between Russian Foreign Minister Sergey Lavrov and US Secretary of State Marco Rubio.

Zelensky has been calling for Ukraine to be given NATO membership as part of any deal to end the crisis, but the Washington-led alliance has been reluctant to make a pledge.

"If there is peace for Ukraine, if you really need me to leave my post, I am ready. ... I can exchange it for NATO," Zelensky said, adding he would depart "immediately" if necessary.

"I want very much from Trump understanding of each other," he said, adding that "security guarantees" from the US president were "much needed".

Zelensky also called for Trump to meet with him before any summit with Putin. He also said there had been "progress" on a deal to give the US preferential access to Ukraine's critical resources.