The US Secretary of State has been in France, as part of her mission to rally support for Georgia.
Condoleezza Rice had talks with President Nicolas Sarkozy and the French foreign minister, whose nation currently holds the EU presidency.
Rice said: â€œLet me just be very clear that the USA stands strongly, and the president of France has just said: for the territorial integrity of Georgia this is a member state of the United Nations whose internationally recognised boundaries have to be respected.
â€œThere will be a process for dealing with what has been a difficult conflict in South Ossetia and in Abkhasia but it proceeds of course from UN security council resolutions that are already there.â€
Rice then left for the Georgian capital.
Sarkozy said: â€œIf tomorrow, Mr Saakashvili signs the document that we negotiated with Mr Medvedev, well then letâ€™s begin the withdrawal of Russian troops. This is what was in doubt. The situation will slowly improve.â€
France is playing a central role in the push for a peace plan.
Riceâ€™s mission was ordered by the US President, with Washingtonâ€™s tone hardening towards Russia.
Meanwhile, the US Defence Secretary Robert Gates said while Washington does not want another cold war, relations with Moscow might be adversely affected for years to come.