The leaders of France and Germany have urged Russia's Vladimir Putin to hold "direct [and] serious negotiations" with Ukraine's president, the German chancellor's office said.
Emmanuel Macron and Olaf Scholz spoke to Mr Putin by phone for 80 minutes.
The pair "insisted on an immediate ceasefire and a withdrawal of Russian troops", the chancellor's office said.
Russia's leader said Moscow was open to resuming dialogue with Kyiv, according to the Kremlin.
It did not mention the possibility of direct talks between Mr Putin and his Ukrainian counterpart, Volodymyr Zelensky.
The Ukrainian president earlier said he was not "eager" for talks, but added they would likely be necessary to end the conflict.
Russian and Ukrainian delegations have held multiple rounds of talks remotely and in person since Russia invaded on 24 February, but efforts have stalled of late.
France and Germany also urged Mr Putin to release 2,500 Ukrainian fighters taken as prisoners-of-war at the Azovstal steelworks in Mariupol.
The sprawling factory became the last holdout in the southern port city, which endured relentless bombardment from Russian forces and now lies in ruins.
Earlier this month, Moscow officials said the last fighters defending the plant had surrendered, while President Zelensky said they had been given permission to leave.
Russia has previously said more than 900 of the fighters were moved to a reopened prison colony in Olenivka, a village in Russian-occupied Donetsk. A smaller number with serious wounds were taken to a hospital in the town of Novoazovsk, also in Donetsk.
Ukraine hopes they will be released as part of a prisoner exchange - but Russia has not confirmed that. Some Russian lawmakers argue the fighters should be tried or even executed.
Also during the call, the French and German leaders asked Mr Putin to lift Russia's blockade of the Ukrainian port of Odesa, to allow for grain exports.
The Kremlin said Mr Putin offered to look at options, to help address the risk of a global food crisis - but demanded that the West lift sanctions.
Russia also warned France and Germany against increasing weapons supplies to Ukraine, saying that could increase instability still further.
This war has created alternate realities
Analysis by Joe Inwood, Ukraine Correspondent
To read the Kremlin's report of the call between Presidents Putin and Macron and Chancellor Scholz, Russia is engaged in a peacekeeping mission in Ukraine. Its actions in the southern port of Mariupol - a city that has been reduced to rubble - are all about "establishing peaceful life" and "liberation".
It is a stark contrast not just with the readout from the EU allies - who said the focus was on the welfare of the 2,500 prisoners-of-war who surrendered - but with the evidence of all independent observers. There are multiple, credible reports of war crimes carried out by occupying Russian forces.
Despite that, the fact that the two most powerful leaders in the EU are holding direct talks with Russia's president is significant.
Their call for a diplomatic solution - even as Russian forces advance in the Donbas - is not supported by all Western allies, who fear it could put pressure on Ukraine to cede territory in return for peace.
It all comes as Moscow claims to have captured the crucial crossroads city of Lyman - and continues its assault of Severodonetsk. The industrial city has been encircled for days - with reports that Ukraine may order a strategic withdrawal of its forces.
It is too soon to say that today's attempts at diplomacy represent a fracturing of the Western alliance… but different positions are beginning to emerge.
In an operational update issued on Sunday, Ukrainian military officials said that intense fighting has continued around the city of Severodonetsk, the easternmost place still under Ukrainian control.
The governor of the Luhansk region, Serhiy Haidai, said two civilians were killed overnight as Russia continued firing heavily on the city with missile and artillery strikes.
On Friday, officials said two-thirds of its perimeter was surrounded by Russian forces.
Mr Haidai had said Ukrainian troops could be forced to withdraw from Severodonetsk, observing: "It is possible that in order not to be surrounded, they will have to leave."
But Yelyzaveta Yasko, a local MP for the region, said on Sunday that Kyiv's troops remained entrenched across the city.
"Severodonetsk for Putin became like one of the places that he really wants to take because he believes that it will give him military power over the whole Donbas region but, as we see that no matter how hard the battles are, still they didn't take it over, all of it," she said.
"But for me very painful to say because we still know and hear about the numbers of the victims that are happening there everyday and unfortunately the situation becomes worse also from the humanitarian side," Ms Yasko observed.
In comments to the BBC on Saturday, Ukraine's Prime Minister Denys Shmyhal said the Russian invasion of his country had destroyed more than 25,000 km (15,000 miles) of roads, several hundred bridges, and 12 airports.
More than 100 educational institutions, over 500 medical facilities, and 200 factories have also been ruined or damaged, he said.
He called for Russia to be forced to pay for "the destruction it has created", saying frozen Russian assets should be transferred to Ukraine to fund reconstruction work.