US Defence Secretary Donald Rumsfeld has called for Russia to withdraw its military forces from Georgia.
Georgia says it has had guarantees from the US
On a visit to Tbilisi he said Moscow had an obligation to withdraw under the terms of four-year-old accords.
The US has expressed support for Georgia's new leaders since mass protests led to the resignation of the former president, Eduard Shevardnadze.
Emergency US funds have already been pledged to help Georgia prepare for fresh presidential polls next months.
The Americans have also been running a $64m programme in Georgia to train and equip its army.
Correspondents say the US is concerned about Georgia's fragile security, partly because it lies on the route of a pipeline that will take oil from Caspian fields through Turkey to European markets.
Mr Rumsfeld met acting president Nino Burdzhanadze amid heightened security following recent bomb attacks, shootings and kidnappings in the Georgian capital.
The Russian military presence was always expected to be on the agenda as its military bases are seen as an obstacle to Georgia's growing ties with the West.
Speaking at a press conference, Mr Rumsfeld said: "As I recall Russia agreed to the Istanbul accords, which suggests to me that there was unanimity on the subject and that would suggest to me that it was probably a pretty good idea. That has been the interest and desire of the government of Georgia."
Mr Rumsfeld also met Georgian presidential candidate Mikhail Saakashvili, who led the opposition protests against Mr Shevardnadze following alleged vote-rigging in parliamentary elections.
"Georgia needs guarantees against any aggressive attempts to influence it from outside," said Mr Saakashvili afterwards.
"The United States has given us its guarantees in this sense. We are hoping that Georgian-US military co-operation in the military sphere will continue. We've got to develop the co-operation program further."
He said he was ready to go to Russia to discuss security interests.
Russia has also been closely monitoring events in Georgia since Mr Shevardnadze was ousted from power on 23 November.
Russian Foreign Minister Igor Ivanov said that both Moscow and Washington were interested in achieving stability and democracy in Georgia.
At a meeting of the Russia-Nato Council in Brussels, he said that "wherever and whenever this or that problem arises, some people immediately forecast that the problem will lead to a worsening of Russian-American relations".
"One gets the impression that there are those who are just keenly waiting for this to happen," he said.
Mr Rumsfeld arrived in Georgia from Afghanistan, where he met interim leader Hamid Karzai and two of the country's main warlords.