The Vatican's Secretary of State told Russian Foreign Minister Sergei Lavrov in a phone call on Tuesday that the Holy See wants armed attacks in Ukraine to stop and humanitarian corridors to be guaranteed.
A Vatican statement said Cardinal Pietro Parolin also repeated the Vatican's willingness "to do anything" to help bring about peace.
The statement said the cardinal told Lavrov that Pope Francis was "deeply worried" about the war.
Parolin appealed "that armed attacks stop and that humanitarian corridors be guaranteed for civilians and rescue workers and that the violence of weapons be substituted by negotiations," the statement said.
Ukrainian civilians began leaving two besieged areas on Tuesday after Russia opened "humanitarian corridors" for them, but Kyiv said Russian forces had shelled an evacuation route from the port city of Mariupol.
Earlier, in its own statement about the call, the Russian foreign ministry said Lavrov set out Moscow's position on the conflict in Ukraine.
Lavrov "outlined the principled Russian position regarding the causes and goals of the special military operation being carried out in Ukraine", the Russian statement said.
Both parties expressed hope that a fourth round of talks between Moscow and Kyiv would be held as soon as possible to agree on the main problems underlying the crisis and to stop hostilities, the Russian ministry added.
Ukraine has said it would welcome Vatican mediation and Parolin, who ranks second to Pope Francis in the Vatican hierarchy, has said previously it is willing to "facilitate" dialogue" between Russia and Ukraine.
Parolin has previously described the war as having been "unleashed by Russia."
Francis has not yet blamed Russia by name publicly but has implicitly rejected Moscow's use of the term "special military operation" for its invasion of Ukraine.
"In Ukraine, rivers of blood and tears are flowing. This is not just a military operation but a war which sows death, destruction and misery," Francis said in his weekly address to crowds gathered in St. Peter's Square on Sunday.
Francis has dispatched two cardinals to help distribute aid to refugees fleeing Ukraine and both have said they will try to enter the country.
The Vatican and the then-Soviet Union began a dialogue in earnest after the fall of the Berlin Wall in 1989, with former Soviet leader Mikhail Gorbachev visiting Pope John Paul II that year.
Full diplomatic relations with Russia were established in 2009 and have been cordial.
Relations between the Vatican and the Russian Orthodox Church were at first spotty after the break up of the Soviet Union but have improved significantly in recent years.
In 2016 Francis became the first pope to meet a leader of the Russian Orthodox Church since the great schism that split Christianity into Eastern and Western branches in 1054.