"We have restarted our relations at a political level, we also agreed to restart the military to military contacts which had been frozen since last August," Scheffer said.
"The Nato-Russia Council is now back in gear. We agreed not to let disagreements bring the whole train to a halt. On Georgia, there are still fundamental differences ... [But] Russia needs Nato and Nato needs Russia."
Scheffer said that the two sides had recognised that it was time to build up joint efforts to tackle common concerns.
"The challenge is to find the areas of co-operation and invest in them, not let areas of disagreement bring all cars in the train to a halt"
"Afghanistan is clearly, also from the Russian side, a dossier where more and closer co-operation is certainly within the range of the possible," he said.
Nato nations are currently discussing with Moscow ways to transport goods through Russian territory to their troops in Afghanistan.
Sergei Lavrov, the Russian foreign minister, was more reserved about the agreement with his Nato counterparts, saying it was "to a certain extent a positive development".
James Appathurai, the Nato spokesman, said earlier on Saturday that the improved relations did not mean that disputes between them were completely resolved.
"Georgia is the big one. The challenge is to find the areas of co-operation and invest in them, not let areas of disagreement bring all cars in the train to a halt," he said.
There have also previously been differences over missile defence, with Moscow voicing strong objections to US plans to base a radar station and interceptor missiles in Poland and the Czech Republic, as well the status of Kosovo and a number of arms treaties.
Moscow sent troops into Georgia after it attempted to reassert its control over the breakaway province of South Ossetia, which receives extensive support from Russia.
Subsequently it recognised the independence of South Ossetia and Abkhazia, another separatist region, further souring relations.
Lavrov said on Saturday that Russia's recognition of the "independence" of the two regions from Georgia was an irreversible "new reality" and the West should get used to it.
An attempt to restore ties in May faltered amid a dispute over Nato's plans to stage joint military exercises with Georgian forces.