"I said during my meeting with [United Nations] Secretary General Ban Ki-moon that work must begin to radically change the format," Mikheil Saakashvili told a meeting with political academics in Tbilisi.
"The current format, after Russia's decision to lift sanctions from Abkhazia, has been destroyed by Russia itself, which has deprived the current format of its legal basis."
However, he said Russia could contribute to a neutral international format.
Moscow earlier this year lifted trade restrictions on Abkhazia and called on other ex-Soviet countries to follow suit.
The Georgian leader said Russia is not a mediator in the conflict, but is a party to the conflict.
Ex-Soviet breakaway regions have stepped up their drives for independence since Kosovo's declaration of independence on February 17. Georgia's Abkhazia and South Ossetia, along with Moldova's Transdnestr, have since asked Russia's parliament, the United Nations and other organizations to recognize their independence.
Both South Ossetia and Abkhazia were involved in bloody conflicts with Georgia after proclaiming independence following the split-up of the Soviet Union in 1991.
Georgia is seeking to regain control of the republics and accuses Moscow of encouraging separatism and interfering in its internal affairs.
Saakashvili proposed a compromise with Abkhazia on its status.
"We offer Abkhazia unrestricted autonomy inside a united Georgian state, full federalism, security guarantees and peaceful development," he said.
"I offer the Abkhaz people the right to veto any amendments to the Constitution and laws of Georgia aimed at preventing the adoption of resolutions that could infringe upon the right to the development of the Abkhaz language, literature, culture and the Abkhaz nation's unique identity," he said.
Last Friday the State Duma, Russia's lower house of parliament, proposed that the president and the government consider the issue of whether to recognize the independence of Abkhazia and South Ossetia.
Peacekeeping in the Georgian-Abkhaz conflict zone is currently carried out by collective CIS forces staffed with Russian service personnel. The Georgian-South Ossetian conflict area is controlled by joint forces also including Russian peacekeepers.