The third round was completed earlier on Friday in Brussels.
The Russian delegation at the talks is led by Russia's EU ambassador Vladimir Chizhov, while the EU delegation is headed by Eneko Landaburu, director general of external relations at the European Commission.
Chizhov said negotiations between the official delegations would be preceded by meetings of working groups, which are due to take place some time in mid-March.
European Union foreign policy chief Javier Solana said on Wednesday it was "too early to say" when a new Russia-EU cooperation agreement would be reached.
The new agreement is set to replace the 1997 Partnership and Cooperation Agreement, which was extended for a year when it expired in December 2007. Talks on a new deal have been repeatedly delayed, initially by Poland and Lithuania and most recently over Russia's August conflict with Georgia over South Ossetia.
A decision to resume the negotiations was made at the Russia-EU summit in Nice on November 14, despite objections from Lithuania.
