Russian President Vladimir Putin and French leader Emmanuel Macron on Friday called for a ceasefire in Libya and a return to dialogue, the Kremlin said after a video conference between the leaders.
On Thursday, France, Germany and Italy called on forces in Libya to cease fighting and for outside parties to stop any interference to try to get talks back on track.
Mr Macron is hopeful of progress in key areas with Moscow, including the crisis in Libya, his office said.
He said on Saturday that he would soon travel to Russia for more talks with Mr Putin.
"Trust-building talks initiated with President Putin at Fort Bregancon continue," Mr Macron tweeted, saying European security, regional conflicts and climate change were key themes.
A senior French presidential official said on Friday that Mr Macron was "confident that we can make progress with Russia on a number of subjects", saying there was "a common interest in the stabilisation of Libya and the reunification of its institutions".
Mr Macron has in recent months pursued rapprochement with Russia, contacting Mr Putin over key areas of disagreement such as Ukraine, in an approach that has discomforted some EU allies.
Mr Putin, noting that it was the 75th anniversary of the signing of the UN charter, spoke of the need to pool efforts to battle common threats such as the coronavirus pandemic, international terrorism and climate change.
He said the call with Mr Macron offered an opportunity to discuss the crises in Ukraine, Syria and Libya, and unresolved tension in the Balkans, among other issues.
"If we want to achieve positive results, we need to combine our efforts," Mr Putin said.
"I know about your intention to organise joint work on many of those issues. We will fully support your proposals."
Mr Putin mentioned a Red Square parade held in Moscow on Wednesday to belatedly commemorate the 75th anniversary of the end of the Second World War in Europe to hail France's contribution to defeating the Nazis.
"We in Russia will never forget the French people who fought alongside our soldiers on the Eastern Front," he said.
Mr Macron, who was due to attend the parade on May 9 before it was postponed because of the pandemic, voiced regret that he was prevented from visiting Moscow.
He paid tribute to the Soviet Union's role in the war.
"The crisis that we have just been through, like all regional crises we've experienced, shows the importance of making the European space, in a broad sense, from Lisbon to Vladivostok, a real space of co-operation and peace," Mr Macron said.
Responding to an invitation from Mr Putin, he said he would be happy to visit "if health conditions allow", possibly at the end of summer.
Mr Macron's office said the video conference was part of an effort launched in August to try to thaw France's relations with Russia, which were damaged by Moscow's annexation of Crimea from Ukraine in 2014.