Russia's 2022 invasion of Ukraine has left tens of thousands of dead, displaced millions and triggered the biggest crisis in relations between Moscow and the West since the 1962 Cuban Missile Crisis.
Orbán, who has faced frequent accusations in the West of being too close to Putin, made the proposals in a call to the Russian leader on Wednesday, the Kremlin and Hungary said, without giving more details.
"The Russian side fully supports Orbán's efforts aimed at finding a peaceful settlement and resolving humanitarian issues related to the prisoner exchange," Kremlin spokesman Dmitry Peskov said.
Russia's Federal Security Service (FSB) had fleshed out details on a potential prisoner exchange to the Hungarian embassy, Peskov said.
Shortly after the Orbán-Putin call, Ukrainian President Volodymyr Zelenskyy criticized the Hungarian leader for undermining Western unity and appeared to mock Hungary's peace efforts by saying he hoped Orbán will not call Assad, the deposed Syrian dictator now living in Moscow, and “listen to his hour-long lectures as well.”
Orbán said it was sad that Zelenskyy clearly rejected the proposals.
UKRAINE CEASEFIRE?
U.S. President-elect Donald Trump, a self-styled master of brokering agreements and author of the 1987 book "Trump: the Art of the Deal," has vowed to swiftly end the conflict but has given no details on how he might achieve that.
On June 14, Putin set out his opening terms for an immediate end to the war: Ukraine must drop its ambition to join military alliance NATO and withdraw troops from four Ukrainian regions claimed and mostly controlled by Russia.
"Russia has never refused peace talks and has repeatedly stated its readiness to resume them on the basis of the Istanbul Agreements of 2022," Peskov said.
Kyiv has insisted that it also needs security guarantees, namely membership in the NATO military alliance that would prevent Russia using a ceasefire to prepare another invasion.
Russia has said it would never accept Ukraine joining NATO - or the deployment of NATO troops on Ukrainian territory.