A second round of direct peace talks between Russia and Ukraine have ended without a major breakthrough, and only a deal to swap more prisoners of war.

Ukrainian negotiators said Russia had again rejected an "unconditional ceasefire" - a key demand by Kyiv and its allies in Europe and the US - but the two committed to return the bodies of 12,000 soldiers.

The Russian team said it had proposed a two- or three-day truce "in certain areas" of the vast front line, but gave no further details.

At Monday's talks, which were held in the Turkish city of Istanbul and lasted just over an hour, the two sides did agree to exchange all sick and heavily wounded prisoners of war, as well those aged under 25.

Expectations were low even before the talks started, with both sides remaining deeply divided on how to end a war that has been raging since Russia launched its full-scale invasion of Ukraine in February 2022.

Moscow currently controls about 20% of Ukrainian territory, including the southern Crimea peninsula it annexed in 2014.

Speaking at a briefing after the meeting, Ukrainian Defence Minister Rustem Umerov, who led Kyiv's negotiating team, said Ukraine was insisting on a "full and and unconditional ceasefire" for at least 30 days on land, at sea and in the air to "end the killings now".

He said Ukraine had handed over its truce proposals to Russia "a few days ago" - but Moscow failed to do the same, presenting its plan only at the talks in Istanbul.

Ukrainian President Volodymyr Zelensky hit back at Russia's proposal of a temporary ceasefire to collect their dead.

"I think 'idiots', because the whole point of a ceasefire is to stop people from becoming dead," he wrote on the social media site, X.

The texts of both the Russian and Ukrainian ceasefire proposals have not officially been made public.

However, Russian state-run media published what they say are key points of Moscow's position after the talks concluded. These include unchanged demands of a Ukrainian military withdrawal from its four partly occupied regions in the south-east, and the demobilisation of its soldiers.

Russia also demands international recognition of Ukraine's Donetsk, Luhansk, Kherson and Zaporizhzhia regions, as well as the annexed Crimea.

Other conditions include a ban on Ukraine's membership in any military alliances, a limit on the size of the Ukrainian army, Russian as an official language, and the lifting of international sanctions on Russia.

Ukrainian Deputy Foreign Minister Serhiy Kyslytsia said that Russia had rejected the unconditional ceasefire.

Ukraine also handed over a list of hundreds of children Kyiv says have been forcefully taken to Russia.

Ukraine's negotiators said they were expecting Russia's response to their proposals by the end of June, stressing the need to prepare for direct talks between Zelensky and Russia's Vladimir Putin.

But so far there is no sign of any progress towards a meeting between the two presidents.

Speaking at a separate news briefing, Russian delegation head Vladimir Medinsky confirmed all sick and heavily wounded prisoners of war, as well as those younger than 25, would be exchanged. No timeframe was given as to when this would happen.

Medinsky also said that Russia would hand over the bodies of 6,000 Ukrainian soldiers to Kyiv next week. Zelensky also said later on Monday that Ukraine would return the bodies of 6,000 Russian soldiers, but did not specify when this would occur.

Rejecting an unconditional ceasefire, Russia prefers to talk about "lasting peace", repeating its previous tough demands which Ukraine and its allies say are tantamount to Kyiv's de facto capitulation.

Zelensky, who was attending a summit in Vilnius, Lithuania on Monday, said that "while there are no meaningful signals from Russia to end the war, it is important to strengthen our defence".

He also called for more pressure through sanctions on Russia.

In the first round of direct peace talks, held on 16 May, Ukraine and Russia failed to bridge their differences on how to end the war, agreeing only to swap 1,000 prisoners of war each.

Zelensky and his European allies have repeatedly accused Russia of deliberately delaying any meaningful negotiations to seize more Ukrainian territory.

US President Donald Trump, who has been pushing for a quick settlement, has so far delayed hitting Russia with tougher sanctions.

However, Trump has indicated that he is "open" to a three-way summit with Zelensky and Putin "if it comes to that", according to White House spokesperson Karoline Leavitt.

"He wants both of these leaders and both sides to come to the table together," she said.

In a rare rebuke last month, Trump called Putin "absolutely crazy" following a massive drone and missile attacks on Ukraine. In response, the Kremlin said Trump was showing signs of "emotional overload".