Ukraine has faced repeated pressure from US President Donald Trump to agree to a deal that could mean painful concessions, as Russian forces pound its power grid and slowly advance on the battlefield.
As the delegations met for a second day at a hotel in the Swiss city, under the mediation of US envoy Steve Witkoff and Trump's son-in-law Jared Kushner, Zelenskiy had called the first day "difficult".
"We can state that Russia is trying to drag out negotiations that could already have reached the final stage," he wrote on X.
Moments after his statement, the delegations broke off the talks and said they would meet again in the future, without providing a date.
Russia's chief negotiator, former culture minister Vladimir Medinsky, described the talks as "difficult, but business-like".
Medinsky - whom Ukrainian officials have accused of engaging in history lectures rather than substantive talks - spoke with the Ukrainians for nearly two hours after formal talks ended, according to a representative of Kyiv's chief negotiator, Rustem Umerov.
A spokesperson for Zelenskiy said the formal part of the talks had addressed territory in Ukraine's east and the fate of the Russian-controlled Zaporizhzhia Nuclear Power Plant, both sticking points since the beginning of the process.
Moscow wants Ukraine to cede the roughly 20 per cent of the eastern region of Donetsk that Russian forces have been unable to conquer - something Kyiv has repeatedly rejected.
Kyiv, meanwhile, wants Zaporizhzhia, Europe's largest nuclear plant, to be operated by the US and Ukraine, which Russia has said is unacceptable.
Tuesday is the fourth anniversary of Russia's full-scale invasion, which has killed hundreds of thousands, driven millions from their homes, and ravaged Ukrainian cities, towns and villages. Russia denies deliberately targeting civilians.
Trump has twice suggested in recent days that it is up to Kyiv to make sure a deal is agreed quickly. He had told reporters on Monday: "Ukraine better come to the table fast. That's all I'm telling you."
In an interview with the US news outlet Axios, Zelenskiy was quoted as saying that it was "not fair" that Trump kept publicly demanding concessions from Ukraine, not Russia.
Zelenskiy also said any plan requiring Ukraine to give up territory that Russia had not captured in the east would be rejected if put to a referendum.
"I hope it is just his tactics and not the decision," Zelenskiy was quoted as saying.
The Geneva meeting follows two rounds of US-brokered talks in Abu Dhabi that made no breakthrough.
Both Zelenskiy and Umerov have made a point of repeatedly thanking the US for its mediation in recent weeks.
Zelenskiy has expressed concern that US Congressional mid-term elections in November could draw Washington's attention away from efforts to end Europe's biggest conflict since World War Two.
In all, Russia occupies about 20 per cent of Ukraine's national territory, including Crimea, seized and unilaterally annexed in 2014.
Ukraine is pushing for its European allies to become more involved in the peace process. Delegations from France, Germany, Britain and others were present in Geneva and were briefed on the talks, but did not take part directly.
