"As long as the withdrawal of troops has not been respected, all meetings on the partnership accord are postponed," Jose Manuel Barroso told reporters after an emergency EU summit in Brussels.
"It is clear that in the light of recent events, we cannot continue as if nothing has happened," he added.
The French president, whose country holds the rotating presidency of the 27-nation bloc, said the EU condemns Russia's actions in Georgia, but does not want to sever partnership relations with Moscow.
"We do not want to cut partnership ties with Russia," Nicolas Sarkozy said. "We condemn in no uncertain terms Russia's disproportionate reaction, but we in Europe realize the need to continue dialogue with our Russian neighbors."
"Let's not launch a Cold War. There's no need to flex our muscles. Demonstrations of force, verbal aggression, sanctions, counter-sanctions - these will not serve anyone," Sarkozy said.
The French president also said European Union member states will provide aid to Georgia, including financial assistance.
"We understand that Georgia is expecting aid from Europe and we will render aid, including financial aid," the president told reporters.
However, he did not clarify when EU aid will be provided.
The EU said earlier on Monday it was making arrangements to send a team of civilian monitors to Georgia to observe adherence to the peace deal brokered by France.
EU foreign policy chief Javier Solana said no Russian approval would be needed for the deployment, which would be made at Georgia's request.
Western powers have criticized Russia's August 26 decision to recognize Abkhazia and South Ossetia as independent states, and have accused Russia of failing to keep to the terms of the peace plan by maintaining peacekeepers in buffer zones in Georgia.
