A source at the Elysée presidential palace said on Sunday that France had suspended its preparations for the summit, due to be held in the Black Sea resort in June, according to the AFP news agency.
Earlier French Foreign Affairs Minister Laurent Fabius called for preparations to be suspended "until our Russian partners have not returned to principles consistent with those of the G7 and G8" on Sunday.
The US and Canada have said they may not go to the summit because of the Russian reaction to Ukraine's toppling of president Viktor Yanukovych.
Calling Russia a "traditional friend", Fabius condemned its "military escalation" and called for mediation, "either directly between the Russians and the Ukrainians or via the UN or the OSCE" (Organisation for Security and Co-operation in Europe).
On Saturday evening French President François Hollande called Russian President Vladimir Putin and appealed to him to "avoid resorting to force", a statement from the Elysée presidential palace reported.
Hollande also spoke to US President Barack Obama, European Council President Herman Van Rompuy and German Chancellor Angela Merkel.
He called for a joint stand "based on respect for Ukrain's territorial integrity and sovereignty, support for the government charged with running the electoral process and recognition of the rights of different communities in Ukraine and Russians ties with the country".
Ukraine on Sunday called up its reservists after Putin obtained the Duma's authorisation to send troops to the country, where tension is running high in ethnic-Russian-majority Crimea.
Kiev also appealed for international observers to monitor its nuclear installatioins.
Troops who appeared to be Russian, although they were wearing no insignia, were reported to be in the region already on Saturday.
The flagship of the Ukrainian fleet, Hetman Sahaydachniy, defected to Russia on Saturday, according to Russian TV channel RT.