Volodymyr Zelensky has said that he was ready to quit as Ukraine's president if it meant Ukraine would be admitted to the NATO military alliance.
Mr Zelensky has faced fierce criticism from the new US administration and said he wants to meet Donald Trump before the US President meets his Russian counterpart Vladimir Putin.
President Zelensky has been calling for Ukraine to be given NATO membership as part of any deal to end the war, 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," Mr Zelensky told a Kyiv press conference, adding he would depart "immediately" if necessary.
Mr Zelensky and President Trump have been engaged in a war of words since US and Russian officials met last week in Saudi Arabia for their first high-level talks in three years.
The move shook the West's policy to isolate the Kremlin and infuriated Ukrainian and European leaders as they were not invited.
In a series of verbal attacks over the last week, Mr Trump has branded Mr Zelensky a "dictator", falsely claimed Ukraine "started" the war and said, contrary to independent opinion polls, that Mr Zelensky was unpopular at home.
Mr Zelensky said 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," President Zelensky told the press conference.
"I want very much from Trump understanding of each other," he said, adding that "security guarantees" from the US president were "much needed".
The Ukrainian leader also called for President Trump to meet with him before any summit with President Putin.
He added that there had been "progress" on a deal to give the United States preferential access to Ukraine's critical resources.
Earlier, the Kremlin hailed dialogue between Donald Trump and Vladimir Putin, whom spokesman Dmitry Peskov called two "extraordinary" presidents, as "promising".
"It is important that nothing prevents us from realising the political will of the two heads of state," Kremlin spokesman Dmitry Peskov told state TV.
Despite Mr Zelensky's push for long-term security assistance and Mr Trump talking up a peace deal, it is unclear whether the US moves can bring Russia nd Ukraine closer to a truce.
Mr Peskov ruled out any territorial concessions as part of a settlement and Russia has repeatedly rejected NATO membership for Ukraine.
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"The people decided to join Russia a long time ago," Mr Peskov said, referring to Moscow-staged votes in eastern Ukraine held amid the offensive that were slammed as bogus by Kyiv, the West and international monitors.
"No one will ever sell off these territories. That's the most important thing," he said.
UN Secretary-General António Guterres meanwhile called for a Ukraine peace deal that respects the country's "territorial integrity".
Mr Putin, in his own comments on the eve of the anniversary of his "special military operation" on Ukraine, said "God" and "fate" were behind his "mission" to defend Russia.
"Fate willed it so, God willed it so, if I may say so. A mission as difficult as it is honourable -- defending Russia, has been placed on our and your shoulders together," he told servicemen who have fought in Ukraine.
"Today, at the risk of their lives and with courage, they are resolutely defending their homeland, national interests and Russia's future," Putin said in a video released by the Kremlin.
Russia's army launched a record 267 attack drones at Ukraine overnight, Ukraine's air force said.
Ukraine shot down or intercepted almost all of them, and there were no reports of major damage.
As its troops advance on the battlefield and it continues massive aerial attacks, Russia has revelled in the diplomat spat between Mr Trump and Mr Zelensky.
"Zelensky makes inappropriate remarks addressed to the head of state. He does it repeatedly," Mr Peskov said.
"No president would tolerate that kind of treatment. So his (Trump's) reaction is completely quite understandable," he said.
Russia's TASS news agency reported that US and Russian diplomats would meet in the next week, a follow-up to Riyadh talks between Russian Foreign Minister Sergei Lavrov and US Secretary of State Marco Rubio.
Scrambling to respond to President Trump's dramatic policy reversal, French President Emmanuel Macron and British Prime Minister Keir Starmer will travel to Washington this week to make the case for supporting Ukraine.
Meanwhile, a march has taken place in Dublin to mark the anniversary of Russia's full-scale invasion.
