Medinsky, a Russian political scientist and former culture minister, led Russia’s negotiating team during the first round of talks on May 16.
The Kremlin earlier rebuffed a call by Ukrainian President Zelenskyy for a three-way summit with Trump and Putin.
Moscow said any meeting involving Russian President Putin and Zelensky would only happen after “concrete agreements” had been struck between negotiators from each side.
‘I am ready for any format’
US President Trump has expressed frustration at both Ukraine and Russia for not yet striking a deal to end the conflict.
The two sides have traded waves of massive aerial attacks in recent weeks, with Ukraine unleashing one of its largest-ever drone barrages on Russia overnight, according to the defence ministry in Moscow.
“If Putin is not comfortable with a bilateral meeting, or if everyone wants it to be a trilateral meeting, I don’t mind. I am ready for any format,” Zelenskyy said in comments to journalists on Tuesday that were published on Wednesday.
The Ukrainian leader said he was “ready” for a “Trump-Putin-me” meeting.
Asked about Zelenskyy’s comments, Kremlin spokesman Dmitry Peskov said: “Such a meeting should be the result of concrete agreements between the two [Ukrainian and Russian] delegations.”
The talks in Istanbul earlier this month failed to yield a breakthrough, but the two sides did agree to a 1000-for-1000 prisoner swap - their largest ever exchange.
Moscow has consistently rejected coordinated Western calls for an immediate ceasefire, while Ukraine has called for more pressure on Moscow to accept a peace deal.
Moscow’s offensive, launched in February 2022, has resulted in tens of thousands of deaths and the destruction of large parts of eastern and southern Ukraine.
The Russian army now controls around a fifth of Ukraine’s territory, including the Crimean peninsula, which it annexed in 2014.
‘Amassing’ troops
Zelenskyy on Wednesday accused Russia of dragging out the peace process and of not wanting to halt its offensive.
“They will constantly look for reasons not to end the war,” he said at a press conference in Berlin alongside German Chancellor Friedrich Merz, criticising Russia for not having agreed to a location for the next round of negotiations.
Zelenskyy also urged allies to invite Kyiv to a Nato summit in June, warning that otherwise it would be a victory for Russia.
Merz said Germany will help Ukraine develop new long-range weapons that can hit targets in Russian territory. Neither leader provided specific details.
The Kremlin said Germany’s support to Kyiv would “hinder peace efforts”.
On the battlefield, Zelenskyy said Russia was “amassing” more than 50,000 troops on the front line around the northeastern Sumy border region, where Moscow’s army has captured a number of settlements as it seeks to establish what Putin has called a “buffer zone” inside Ukrainian territory.
Russia’s army said on Wednesday it had captured another village in the Sumy region.
-Agence France-Presse
