Those two republics both run their own affairs, but their self-declared autonomy is not recognized internationally. UN peacekeepers act as monitors on the de facto border between Georgia and Abkhazia.
Saakashvili has vowed to bring both regions under Tbilisi's control.
Speaking to reporters after his meeting with Saakashvili, Annan said the United Nations would continue efforts to find a solution to the problem of Georgia's breakaway republics.
Annan urged all sides to show patience and respect for the rule of law until a suitable compromise could be found.
Annan made a brief stopover in Georgia on his way from Pakistan to the United States.
(with additional wire reports)