Putin also emphasised that the "complete cessation of foreign military assistance and the provision of intelligence information to Kyiv" was a condition for any permanent peace deal.
In a statement, the White House said negotiations on a maritime ceasefire in the Black Sea, as well as other potential areas of concern, would commence immediately in the Middle East.
"The leaders agreed that the movement to peace will begin with an energy and infrastructure ceasefire, as well as technical negotiations on implementation of a maritime ceasefire in the Black Sea, full ceasefire and permanent peace," the White House readout said.
Meanwhile, AFP is reporting Russia and Ukraine will swap 175 prisoners of war each on Wednesday, quoting the Kremlin.
Trump had been pressuring Putin to agree to a 30-day ceasefire that he hopes would move one step closer to ending Europe's biggest conflict since World War II. The war has killed or wounded hundreds of thousands of people, displaced millions and reduced entire towns to rubble.
Trump has hinted that a permanent peace deal could include territorial concessions by Kyiv and control of Ukraine's Zaporizhzhia nuclear power plant.
The US president's overtures to Putin since returning to the White House in January have left traditional US allies wary.
Ukraine and its Western allies have long described Russia's invasion of Ukraine as an imperialist land grab, and Ukrainian President Volodymyr Zelensky has accused Putin of deliberately prolonging the war.
Zelensky, who arrived in Finland on Tuesday to discuss the NATO state's support for Ukraine, says Ukraine's sovereignty is not negotiable and Russia must surrender the territory it has seized. He says Moscow's ambitions will not stop at Ukraine if it is allowed to keep the territory it has seized.
European Commission President Ursula von der Leyen warned on Tuesday that Russia had massively expanded its military-industrial production capacity in preparation for "future confrontation with European democracies".
Speaking to Trump late on Monday, British Prime Minister Keir Starmer "reiterated that all must work together to put Ukraine in the strongest possible position to secure a just and lasting peace," the British leader's spokesperson said.
Russia seized the Crimea peninsula from Ukraine in 2014 and most of four eastern Ukrainian regions following its invasion in February 2022. All told, it controls about a fifth of Ukrainian territory.
Putin said he sent troops into Ukraine because NATO's creeping expansion threatened Russia's security. He has demanded Ukraine drop any ambition of joining the Western military alliance.
Putin has also said Russia must keep control of Ukrainian territory it has seized, Western sanctions should be eased and Kyiv must stage a presidential election. Zelenskiy, elected in 2019, has remained in office under martial law he imposed because of the war.
