"You've got a solid friend in America," Bush said in the capital Tbilisi on Tuesday.
He encouraged Georgian President Mikhail Saakashvili to use peaceful means to settle disputes with two separatist regions - Abkhazia and South Ossetia - which are aligned with Moscow, but offered to help resolve the disputes if assistance was requested.
Bush and Saakashvili met in the Parliament House about two blocks from Freedom Square where tens of thousands of people gathered to see or hear the US leader.
"You've got a solid friend in America"
US President George Bush to Georgia's president
"No event in the history of this country has ever assembled anything close to these numbers," Saakashvili said.
"It shows the importance of this visit."
Bush said he talked in Moscow with Russian President Vladimir Putin about Georgia's demand for the closure of two Russian bases in this country.
"He (Putin) reminded me that there is an agreement in place - a 1999 agreement," Bush said. "He said that the Russians want to work with the [Georgian] government to fulfil their obligations in terms of that agreement.
"I think that's a commitment that's important for the people of Georgia to hear. It shows there's grounds to work to get this issue resolved."
The long-simmering dispute over the bases has strained relations between the former Soviet republic, relations that have soured further since Saakashvili and his pro-Western administration came to power in 2004.
Bush offered Saakashvili (R) help
to resolve separatist disputes
Georgia wants Russia to withdraw two Soviet-era holdover bases it retains in Georgia.
Russian Defence Minister Sergei Ivanov said it could take up to four years to build the barracks, garages and other infrastructure in Russia to handle the servicemen and materiel withdrawn from Georgia.
Saakashvili did not attend Monday's Victory Day celebrations in Moscow to protest over Russia's reluctance to withdraw from the two bases.
Bush also said that Russia would benefit from the emergence of new democracies in neighbouring countries of the former Soviet Union.
"When you have peaceful countries on your border, you benefit," Bush said.
"I'm sure that Russia will recognise the benefits of having democracies on her borders."