There was no anticipation of significant progress on ending the war at the Tuesday-Wednesday meeting in Switzerland.
Both sides appear to be sticking to their negotiating positions on key issues, despite the United States setting a June deadline to reach a settlement.
The future of Ukrainian land that Russia occupies or still covets is a central issue.
Ukrainian defenders remain locked in a war of attrition with Russia's bigger army along the roughly 1250-kilometre front line.
Ukrainian civilians endure Russian aerial barrages that repeatedly knock out power and smash homes, while Ukraine has developed drones that can fly deep into Russian territory and strike oil refineries and arms depots.
The governor of western Russia's Bryansk region said Monday that air defences had shot down 229 Ukrainian drones in the previous 24 hours.
No other Russian region has come under as many simultaneous drone attacks in a single day, Governor Alexander Bogomaz said.
Ukraine's Air Force, meanwhile, said Russia launched 62 long-range strike drones and six missiles of various types at Ukraine overnight.
Kremlin spokesman Dmitry Peskov said Monday that the talks in Geneva will deal with a "broader range of issues related to the territories and other issues connected to the demands that we have".
He didn't elaborate on the issues.
A year of peace efforts by US President Donald Trump's administration has failed to stop the fighting.
Western officials and analysts say Russian President Vladimir Putin believes that time is on his side, that western support for Ukraine will peter out and that Ukraine's resistance will eventually collapse under pressure.
General Kyrylo Budanov, Ukrainian President Volodymyr Zelenskiy's chief of staff, posted a photograph on Telegram showing himself standing next to a train with other members of the negotiating team, which is due to be led in Geneva by Rustem Umerov, Ukraine's National Security and Defence Council chief.
Entering or leaving Ukraine entails a long overland journey, even for VIPs, as the country's airspace is closed because of the war.
Putin's adviser Vladimir Medinsky, who headed Moscow's team of negotiators in the first direct peace talks with Ukraine in Istanbul in March 2022 and who has forcefully pushed Putin's war goals, is returning to lead Moscow's delegation.
Medinsky has written several history books that focus on exposing purported Western plots against Russia and denigrate Ukraine.
Igor Kostyukov, the head of Russian military intelligence, and Deputy Foreign Minister Mikhail Galuzin, along with other officials, will also be in the delegation, Kremlin spokesman Peskov said.
Putin's envoy Kirill Dmitriev will also travel to Geneva for separate talks with the US on economic cooperation, according to Peskov.
Moscow and Kyiv are keen to offer future business opportunities to Washington.
It was not clear which American officials would be in Geneva.
At recent talks in Abu Dhabi, the capital of the United Arab Emirates, the Trump administration was represented by envoys Steve Witkoff and Jared Kushner.
The Russian and Ukrainian delegations were to report back to their leaders before any possible compromises discussed in Geneva could be accepted.
