Mr Medvedev spoke of re-equipping Russia's military
Russian President Dmitry Medvedev has said the US should join Russia in combating terrorism, rather than supporting "rotten regimes".
Speaking on the anniversary of 9/11, Mr Medvedev pledged full co-operation with the US on anti-terrorism.
But he said the US should reconsider its ties with regimes that "conduct military adventures", in a clear reference to Georgia's government.
He said Russia would focus on rearming after the Georgian conflict last month.
Russia and Georgia clashed briefly over the breakaway regions of Abkhazia and South Ossetia.
After five days of fighting a ceasefire was agreed - but each side has accused the other of breaching the accord.
'No imperial ambitions'
Russia, which has backed self-declared governments in the nominally Georgian regions for years, recently infuriated the West by recognising their independence.
Kremlin officials have been involved in a bitter war of words with the US throughout the crisis.
Moscow has repeatedly accused Washington of arming Georgia. The US says Russia is violating Georgia's sovereignty.
The Georgian government, meanwhile, has accused Moscow of attempting to annex the two provinces.
Some critics have even suggested that Russia wanted to re-establish its spheres of influence from the Cold War era, and planned to target Ukraine's pro-Western government next.
But Prime Minister Vladimir Putin has once again angrily denied those claims.
"We do not have and will not have any of the imperial ambitions that people accuse us of," Mr Putin said from the southern resort of Sochi.
At a Kremlin meeting Mr Medvedev said the anniversary of the 9/11 attacks was a "sorrowful day for the USA and for all the other countries which suffer from terrorism".
He said that Russia was ready for "co-ordinated, fully-fledged co-operation with the USA and other states on issues of the fight against terrorism".
But he added: "We consider this our primary task and we believe that it is much more useful to the USA than developing relations with rotten regimes which undertake military adventures."
Mr Medvedev's remarks come a day after Chechen President Ramzan Kadyrov accused the US of attempting to start a war in the Caucasus.
Mr Kadyrov, a Moscow supporter, accused the US of using the Caucasus as a testing ground to challenge Russia's resolve.
Fighting between Russia and Georgia began on 7 August after the Georgian military tried to retake the breakaway region of South Ossetia by force.
Russian forces launched a counter-attack and the conflict ended with the ejection of Georgian troops from both South Ossetia and Abkhazia.