Mr Sarkozy said the EU had to re-examine its relationship with Russia
European Union leaders have agreed to suspend talks on a new partnership agreement with Moscow until Russian troops have withdrawn from Georgia.
EU Commission President Jose Manuel Barroso said it was clear it could not "continue as if nothing had happened", after an emergency summit in Brussels.
The EU also condemned Russia's move to recognise the independence of Georgia's regions of South Ossetia and Abkhazia.
Russia said the talks suspension had damaged the credibility of the bloc.
"It is more of a self-punishment for the European Union because this does not improve the EU's credibility as a negotiating partner," Russia's envoy to the EU, Vladimir Chizhov, said.
Earlier, Russian Foreign Minister Sergei Lavrov warned the EU and the US that further support for Georgia would be a "historic" mistake.
Mr Lavrov also called for an embargo on arms supplies to Tbilisi until a different government was in place there.
The EU's foreign policy chief, Javier Solana, meanwhile said it was prepared to send hundreds of civilian monitors to Georgia to check if Russia was abiding by the EU-brokered ceasefire agreement.
Fighting between Russia and Georgia began on 7 August after the Georgian military tried to retake South Ossetia by force.
Russian forces launched a counter-attack and the conflict ended with the ejection of Georgian troops from South Ossetia and Abkhazia.
Speaking after EU leaders met in Brussels to discuss the crisis, Mr Barroso and French President Nicolas Sarkozy announced they had agreed to postpone talks on an EU-Russia partnership deal.
The timing of the talks, originally scheduled for mid-September, would depend on Russian forces moving back to their pre-7 August positions, he added.
Mr Sarkozy, whose country is the current holder of the EU presidency, said the crisis meant the bloc had to re-examine its relationship with Russia.
"The EU would welcome a real partnership with Russia, which is in the interests of all, but you have to be two to have a partnership," he said.
The French president also announced that he would visit Moscow on Monday along with Mr Barroso and EU foreign policy chief Javier Solana for a "crucial" meeting with the Russian government.
A joint statement from the EU summit said the European Council was gravely concerned by the "disproportionate reaction of Russia" in Georgia, and called on other states not to follow Russia's lead by recognising the independence of South Ossetia and Abkhazia.
"We are convinced that it is in Russia's own interest not to isolate itself from Europe," it added.
Dmitry Medvedev warned Moscow would retaliate against any sanctions
There was also a strong signal of support for Georgia, with EU-wide backing for a donors' conference for reconstruction, the promise of a free trade area and fewer travel restrictions on its citizens.
To coincide with the summit, Georgians held several rallies across their country and in other European capitals, at which they called for further Western support and assistance.
President Mikhail Saakashvili told a crowd of thousands in Tbilisi's Freedom Square that Georgia was "united as never before" and urged EU leaders not to give up in the face of Russian "aggression".
Earlier, Mr Lavrov warned the US and its allies that supporting President Saakashvili would be a historic mistake, and called for an arms embargo "while a different government turns Georgia into a normal state".
"To protect the region from the recurrence of violence, Russia will continue taking measures to punish the guilty, so that this regime is never able to do evil," he said.
Speaking in Moscow, Mr Lavrov said Russia had returned to the world stage as a responsible state which could defend its citizens.
Mr Lavrov's comments follow Mr Medvedev's redefining of Russia's foreign policy principles.
Russia, the Kremlin leader declared, would no longer accept a situation whereby a single country, like the US, sought global domination.
Mr Medvedev also pledged to defend the lives and dignity of Russian citizens, wherever they are located.
He made it clear that there were parts of the world where Russia sees itself as having privileged interests.