Georgia dismissed the move as a "show aimed at creating the illusion of a withdrawal".
The conflict broke out on 7 August when Georgia launched an assault to wrest back control of the Moscow-backed breakaway region of South Ossetia, triggering a counter-offensive by Russian troops who advanced beyond South Ossetia into Georgia's heartland.
A ceasefire was signed at the weekend, with Moscow pledging to begin pulling back its troops on Monday, but correspondents say there has so far been little sign of any large-scale withdrawal.
Both sides have accused the other of violating the EU-brokered peace plan.
Following the crisis talks in Brussels, the 26 foreign ministers said in a joint statement that they could not have normal relations with Russia as long as Moscow had troops in Georgia.
No more use of force
Stop all military actions for good
Free access to humanitarian aid
Georgian troops return to their places of permanent deployment
Russian troops to return to pre-conflict positions
International talks about security in South Ossetia and Abkhazia
"The Alliance is considering seriously the implications of Russia's actions for the Nato-Russia relationship," the statement said, read out by Nato Secretary General Jaap de Hoop Scheffer.
"We have determined that we cannot continue with business as usual."
Mr de Hoop Scheffer added that he could not see how the Nato-Russia Council - set up in 2002 as a framework for dialogue - could convene at this time.
But he said lines of communication would not be abandoned.
"The future of our relations with Russia will depend on the concrete actions Russia will take to abide by the words of President Dmitry Medvedev [regarding the peace plan], which is not happening at the moment," Mr de Hoop Scheffer said.
Jaap de Hoop Scheffer has warned Russia that there "will be no business as usual"
He also said that the member states had agreed to set up a Nato-Georgia commission to strengthen ties with Tbilisi, but stopped short of giving a timetable for Georgia's accession to Nato.
The Russian military has warned that the withdrawal process will be slow until the weekend at least, and that troops will remain in an undefined buffer zone around South Ossetia.
It says such a move is permitted under the ceasefire deal which allows Russia to take additional security measures until international peacekeepers are deployed.
But Georgia says Moscow is going much further and that Russian troops have seized control of a key commercial port in Poti in an attempt to cripple the Georgian economy.
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