Abkhazia: Georgia offers peace to regions
Speaking at an Independence Day rally, he said he was ready to begin peace talks over any federal state model acceptable to the breakaway regions.
South Ossetia and Abkhazia took to arms after Georgia's independence from the Soviet Union in 1991.
The president has said he wants to see a united Georgia.
Earlier this month, the rebel region of Ajaria, on the Turkish border, returned to Tbilisi's control after mass demonstrations forced the resignation of its separatist leaders.
On Wednesday, Georgia celebrated its Independence Day by holding the biggest military parade in the country's history.
But amid the show of force, the president spoke of peace. He called on Georgians to remember their own mistakes and to show understanding and tolerance towards the people of Abkhazia and South Ossetia.
Speaking in the Ossetian and Abkhaz languages, he said: "For the first time, I would like to address the issue of a special status, and to guarantee all rights for security to our brothers.
"We have to build new relations based on understanding and friendship."
Following Georgia's independence from the Soviet Union in 1991, South Ossetia and Abkhazia fought bloody wars with Georgia and have, since then, retained powers of local control independent from Tbilisi.
A parliamentary election in South Ossetia at the weekend resulted in victory for the party of the region's pro-Russian president, Eduard Kokoity.
The BBC's Natalia Antelava, in Tbilisi, says Mr Saakashvili may feel empowered by his recent success in Ajaria, but South Ossetia and Abkhazia present an entirely different problem.
She says the people there are ethnically different from the Georgians, their memories of war are still vivid, and both provinces want to unite with neighbouring Russia.
Analysts have already hailed Mr Saakashvili's Independence Day remarks as the single most important step towards peaceful resolution of these stagnant conflicts.
But making peace with Abkhazia and South Ossetia, they say, will take much more then a few phrases in the native languages.