But EU leaders failed to convince Medvedev that their planned partnership with Belarus, Ukraine, Moldova, Georgia, Armenia and Azerbaijan, was intended only to promote "prosperity and stability".
"I`ll put it succinctly. We tried to convince ourselves but in the end we couldn`t," Medvedev said.
"What bothers us is that for some [ex-Soviet] states this is seen as a partnership against Russia."
Nicu Popescu, a research fellow at the European Council on Foreign Relations, told Al Jazeera that he did not believe Russia had any serious reasons to be concerned about the EU pact with the former Soviet states.
"What irritated Moscow was that the European Union put pressure on Belarus not to recognise Abkhazia and South Ossetia [breakaway Georgian regions] as well as the deal with Ukraine on the reconstruction of the Ukrainian pipeline," he said.
"These two factors mobilised Russia against the eastern partnership in a way that exaggerated it given the low-scale nature of the European policy."
The two sides also failed to agree on measures to prevent gas supplies to Europe being cut again, following a dispute between Ukraine and Russia in January that left millions of people without heat.
Medvedev insisted that Ukraine was solely to blame for the dispute, and warned that disruptions could occur again if Kiev could not pay.
"We are ready to help the Ukrainian state but we would like a significant part of that work to be perhaps taken on by the European Union," he said.
Jose Manuel Barroso, president of the European Commission, said it was up to Russia, not just Ukraine, to ensure reliable supplies to Europe.
"Disruption in the export and transport of gas must not be allowed to occur again," he said.
"We ask Russia and Ukraine to do everything in their power to prevent another crisis next year."
Despite continuining tension between the EU and Russia, the talks "increased our mutual trust, which is very much needed and very important," Vaclav Klaus, the Czech Republic president, whose country holds the EU presidency, said.
"The European Union considers Russia to be its strategic partner. We must do something to make this real and not just a formal proclamation," he said.
Barroso said Russia and the EU had made "some good progress" toward a new agreement to strengthen ties and replace a formal pact that expired in 2007.
The EU suspended talks on the deal after Russia`s war with Georgia in August, but announced in November that it would return to the