The warring sides met for about an hour in the Turkish city of Istanbul, for only the second such round of negotiations since March 2022.
Turkish President Tayyip Erdogan described it as a great meeting and said he hoped to bring together Russian President Vladimir Putin and Ukrainian President Volodymyr Zelenskiy for a meeting in Turkey with US President Donald Trump.
But there was no breakthrough on a proposed ceasefire that Ukraine, its European allies and the US have all urged Russia to accept.
Russia says it seeks a long-term settlement, not a pause in the war; Ukraine says Putin is not interested in peace.
Kremlin aide Vladimir Medinsky said Russian negotiators had handed their Ukrainian counterparts a detailed memorandum outlining Russia's terms for a full ceasefire.
Medinsky, who heads the Russian team, said his side had also suggested a "specific ceasefire of two to three days in certain sections of the front" so that the bodies of dead soldiers could be collected.
Each side said it would hand over the bodies of 6000 dead soldiers to the other.
In addition, they said they would conduct a further big swap of prisoners of war after 1000 captives on each side were traded following a first round of talks in Istanbul on May 15.
Ukrainian Defence Minister Rustem Umerov, who headed Ukraine's delegation, said the new exchange would focus on those severely injured in the war and on young people.
Umerov also said that Russia had handed a draft peace accord to Ukraine and that Ukraine - which has drawn up its own version - would review the Russian document.
Ukraine has proposed holding more talks before the end of June but believes that only a meeting between Zelenskiy and Putin can resolve the many issues of contention, Umerov said.
Zelenskiy's chief of staff, Andriy Yermak, said Ukraine's delegation had requested the return of a list of children who it said had been deported to Russia.
Russia says such children were moved in order to protect them from fighting.
Medinsky said there were 339 names on Ukraine's list but that the children had been "saved" not stolen.
In Russia, before the talks began, angry war bloggers called on the country's armed forces to deliver a fearsome retaliatory blow against Ukraine after it launched an attack on Sunday targeting Russian nuclear-capable long-range bombers in Siberia and elsewhere.
Ukraine and Russia have issued starkly different assessments of the damage done to Russia's fleet of strategic bombers - a key element in its nuclear arsenal - but it was clear from publicly available satellite imagery that Russia's military had suffered some serious equipment losses.
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