"I hope that our discussion today will be fruitful and the results will allow Russia to enter the WTO by the end of the year, in December," Calmy-Rey told President Dmitry Medvedev in his residence just outside Moscow.
Medvedev responded by saying Russia "also very much wants that", and heaped praise on Swiss mediation efforts at the meeting, which was hastily organized over the weekend.
Russia is closer than ever to joining the WTO after being offered a "take it or leave it" compromise last week by its tiny neighbor Georgia, the last holdout in Moscow's bid.
Joining the 153-member trade bloc has been an ambition of Prime Minister Vladimir Putin, who is seeking a return to the presidency in a March 2012 vote.
Georgia, like all WTO members, has an effective veto on Russia's membership, which it has threatened to use unless a dispute with Russia over customs controls was resolved.
Russia humiliated ex-Soviet Georgia in a brief 2008 war over Georgian breakaway region South Ossetia. They have not restored diplomatic relations.
Russia said on Thursday it needed several days to review a proposal on border trade with Georgia made by Swiss mediators.
Russian entry to the WTO would be the biggest step in world trade liberalization since China joined a decade ago, and the United States and the European Union have urged all sides to try to settle membership terms by the end of this year.
Russia's President Dmitry Medvedev shakes hands with his Swiss counterpart Micheline Calmy-Rey during their meeting at the Gorki presidential residence outside Moscow (Photo: Reuters)