"We want American support for NATO, we want American support for further European integration at this very difficult moment for Georgia's democracy and Georgia's survival," the president added.
Tbilisi, which broke off diplomatic relations with Russia following the 2008 war, says Moscow is making efforts to prevent it from joining NATO and the EU.
Russia and Georgia fought a brief war in 2008 after Tbilisi launched a major offensive against the independence-seeking republic of South Ossetia in a bid to retake control of the region.
Russia, South Ossetia's main ally, responded to the attack by moving in its military forces and driving out Georgian troops from both South Ossetia and Abkhazia.
The two regions declared independence after the fall of the Soviet Union in the early 1990s, but were not internationally recognized.
In August 2008, Russia recognized Abkhazia and South Ossetia as sovereign states.
US Secretary of State John Kerry has expressed Washington's support for a bid by Georgia to join the North Atlantic Treaty Organization (NATO) and the European Union.
"We are very supportive of Georgia's aspirations with respect to NATO and to Europe," Kerry said at a joint press conference with visiting Georgian President Mikheil Saakashvili on Wednesday.
Saakashvili, whose terms expire in October, also called on the United Nations to help the former Soviet Union republic achieve NATO and EU membership.