Russia said on Tuesday that it would re-start supplies but shipments have not yet reached Europe, much of which has been without gas during a bitter winter.
'No positive outcome'
Medvedev said on Saturday that bilateral talks in Moscow would continue and that he wanted supplies to resume "in the next few days".
Neave Barker, Al Jazeera's correspondent in Moscow, said: "What Russia was keen to push across ... was that this was no longer a bilateral issue between the Ukraine and Russia.
"That's because the entire continent was involved and therefore European partners, those countries hard hit in eastern Europe and representatives from the European Union, should get involved in trying to end this situation.
"Unfortunately, no positive outcome has happened and it may no longer be business as usual for Ukraine and Russia at the European Union," he said.
The EU has warned the two countries that its relations with them would be reviewed if the dispute is not resolved this weekend.
Yulia Tymoshenko, the Ukrainian prime minister, attended the meeting, with Medvedev, Vladimir Putin, the Russian prime minister, and top level delegates from gas companies, the EU and European nations affected by the dispute.
EU monitoring teams have been deployed in the Ukraine and Russia to oversee the safe transit of supplies.
Ukraine, an ex-Soviet state with pro-Western leaders, has also angered the Kremlin in the past months because of its attempts to join Nato.
The European Union relies on Russia for about one quarter of all the natural gas it needs, with 80 per cent being pumped via pipelines crossing Ukraine.