Talks aimed at advancing toward a broader peace plan will begin immediately, the White House said following a lengthy call between the two leaders.
Putin ordered the Russian military to stop attacks against energy sites after speaking with Trump, the Kremlin said in a statement.Â
But he again raised concerns during the call that a temporary ceasefire might allow Ukraine to mobilise more soldiers and rearm itself.
Putin also emphasised that any resolution of the conflict would require an end to all military and intelligence assistance to Ukraine, the Kremlin added.
Ukrainian President Volodymyr Zelenskiy said on Tuesday that Ukraine would support a US proposal to stop strikes on Russian energy infrastructure, and said he hoped to speak to Trump about his talks with Putin.
"I think it will be right that we will have a conversation with President Trump and we will know in detail what the Russians offered the Americans or what the Americans offered the Russians," Zelenskiy told reporters during an online briefing.
Russian forces are advancing in Ukraine's east and pushing back Ukrainian troops from Russia's Kursk region.
Negotiations on a maritime ceasefire in the Black Sea, as well as a more complete ceasefire and a permanent peace deal, will commence immediately in the Middle East, the White House said in a statement.
In a social media post after the call, Trump said he and Putin had agreed to work quickly toward a ceasefire and eventually a permanent peace agreement.
"Many elements of a Contract for Peace were discussed, including the fact that thousands of soldiers are being killed, and both President Putin and President Zelenskyy would like to see it end," he wrote, using an alternate spelling for the Ukrainian leader.