Mr Medvedev and his Foreign Minister Sergei Lavrov told Georgia's president that joining the alliance would lead to a "spiral of confrontation".
Mr Medvedev said Ukraine would be in breach of a friendship treaty if it joined Nato, Mr Lavrov said.
The leaders are at a summit of 12 ex-Soviet states in St Petersburg.
Conflicts
Georgia has been pushing for entry to Nato and the European Union, straining relations with Russia.
Tensions have also grown over Russia's support for separatists in Georgia's breakaway regions of Abkhazia and South Ossetia.
Both Russia and Georgia have accused each other of preparing for war in Abkhazia.
"We reiterated our strong interest in seeing those conflicts resolved," Mr Lavrov said, following the meeting with Mr Saakashvili at the Commonwealth of Independent States informal summit.
"We stated this could not be achieved by moving Georgia artificially into Nato because this would lead to another spiral of confrontation in the area."
The Georgian president played down talk of confrontation, saying the problem could be resolved with "goodwill".
'Security risks'
Analysts had been waiting to see if Mr Medvedev's relations with Ukraine and Georgia would be warmer than those under his predecessor, Vladimir Putin. But the new president stuck to the same line as Mr Putin when he met President Viktor Yushchenko of Ukraine on Friday.
He pointed to a 1997 friendship treaty between Russia and Ukraine.
"The treaty... contains the obligation on the two parties not to do anything which would create threats or risks for the security of the other party," Mr Lavrov told reporters.
"This was reiterated by President Medvedev, that we do not believe Nato membership for Ukraine would serve... the interests of the two countries."
Mr Medvedev also warned Mr Yushchenko not to expel the Russian navy from the base it leases at Sevastopol on Ukraine's Black Sea coast, as it has threatened to do.
And he said Russia would almost double the price it charges neighbouring Ukraine for gas from 1 January, 2009.
Mr Lavrov denied the move was political, saying it was forced by increasing costs in Central Asia. The two countries have had several recent disputes over gas, with Russia cutting supplies and Ukraine alleging Moscow uses gas as a political weapon.
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