France says Russian President Vladimir Putin has agreed on the need to "prioritise a diplomatic solution" to the crisis over Ukraine and secure a ceasefire in the east of the country, BBC reported.
In a phone call with President Emmanuel Macron, Mr Putin also agreed that foreign ministers from both countries would meet "in the coming days".
Western nations believe Russia is ready to invade Ukraine, which Moscow denies.
Meanwhile, Ukraine says talk of an imminent invasion is "inappropriate".
President Macron's call on Sunday was the latest effort to prevent military action by Russia, which has amassed tens of thousands of troops on Ukraine's borders.
It came amid increased clashes between Ukrainian forces and Russian-backed rebels in Ukraine's eastern Donbas region.
Hours later, the French presidency said a second phone call between Mr Macron and Mr Putin took place, following a conversation between Mr Macron and US President Joe Biden.
Mr Macron proposed a summit between Mr Biden and Mr Putin, the statement said, and both leaders had accepted "the principle" of such a meeting, to be held on the condition that Russia does not invade Ukraine.
Details would be discussed during a meeting between US Secretary of State Antony Blinken and the Russian Foreign Minister, Sergei Lavrov, on Thursday.
