"If (it means) peace for Ukraine, if you really need me to leave my post, I am ready," an irritated-looking Zelenskiy said when asked during a press conference whether he was ready to leave his post if it meant securing peace.
"I can exchange this for NATO (membership), if that condition is there, immediately," the president added.
US President Donald Trump has pushed for elections to take place in Ukraine, having branded Zelenskiy a "dictator", an apparent reference to the Ukrainian leader's official five-year term running out in 2024. Russia has cited this in the past to assert that he is an illegitimate leader.
Ukrainian legislation prohibits holding elections during a state of martial law, which Ukraine declared the day Russia invaded in February 2022. Trump also falsely claimed that Zelenskiy has an approval rating of four per cent.
"I am not going to be in power for decades, but we will not allow Putin to be in power over the territories of Ukraine either," Zelenskiy said on Sunday, referring to Russian President Vladimir Putin.
A poll released this week put Zelenskiy's approval ratings at 63 per cent, and he made reference to this when talking about Trump's claims on Sunday, calling his false statements "dangerous".
"I believe it's not a mistake, it's misinformation that has an impact," Zelenskiy said.
Zelenskiy said earlier this week Trump was in a "disinformation bubble", angering the US President and his team. On Sunday, he sought to justify the earlier comments.
"(The information) about four per cent of Ukrainians supporting me is one of the signals spread by the Russians, that's why I said it was a disinformation attack, I didn't say it was President Trump," Zelenskiy said on Sunday.
Trump's criticism of Zelenskiy came as relations between the two leaders deteriorated sharply in recent weeks.
Zelenskiy opposes the idea of elections in a full-scale war, a position backed by his major domestic political opponents.
The Ukrainian president also said he wanted to see Trump as a partner for Ukraine and more than a simply a mediator between Kyiv and Moscow.
"I really want it to be more than just mediation... that's not enough," he told a press conference in Kyiv.
Trump has said Ukraine should give the US $US500 billion ($A787 billion) in critical raw materials as payback for aid which Kyiv has already received from the previous Joe Biden administration.
Zelenskiy declined to sign a detailed US proposal last week that would have seen Washington receiving 50 per cent of Ukraine's critical minerals, which include graphite, uranium, titanium and lithium, the latter a key component in electric car batteries.
He has said he wants to do a deal, but that it should offer security guarantees for Ukraine in return.
On Friday, he said US and Ukrainian teams were working on a deal and Trump said he expects a deal will be signed soon.
On Sunday, Zelenskiy said at the press conference that he rejected the idea that Ukraine owed the US $US500 billion ($A787 billion).
"There cannot be (any) format which makes us debtors for the old (aid given)."
Zelenskiy said earlier this week that Washington had supplied his country with $US67 billion ($A105 billion) in weapons and $US31.5 billion ($A49.6 billion) in direct budget support throughout the nearly three-year war with Russia.
"I will not sign what 10 generations of Ukrainians will be repaying," Zelenskiy said of the minerals deal.
Ukraine's economy minister Yuliia Svyrydenko said on Sunday the 18 per cent of Ukraine under Russian occupation contained about $US350 billion ($A551 billion) of critical raw materials, adding that Ukraine is conducting additional geological research to update decades-old information.
