Relations between Europe and Russia soured under Medvedev's predecessor Vladimir Putin over a range of issues, including energy and democratic freedoms. Medvedev pledged in his inauguration speech in May to promote the rule of law, free speech and human rights.
In an interview ahead of a EU-Russia summit in West Siberia on Thursday and Friday, Javier Solana said: "This will be our first summit with President Medvedev leading the Russian delegation. We very much look forward to continuing and deepening our cooperation with Russia under the Medvedev presidency."
The summit in Khanty-Mansiisk is expected to lay the groundwork for talks on a long overdue comprehensive cooperation pact.
"The launch of negotiations for a new EU-Russia Agreement will undoubtedly be the main result of this summit," Solana said.
Europe has sought free access to Russian energy resources. Russia, the EU's key supplier of oil and gas, will press for more access to European markets and for visa-free travel for its citizens. European officials are also expected to highlight what they call Russia's backsliding from democracy.
"It is in our common interest to negotiate a new agreement which reflects the depth of our relationship today, rather than our relations ten years ago," Solana said.
Talks on the agreement were first postponed because of Russia's embargo on Polish meat. When the dispute was resolved, obstacles came from Lithuania, which demanded tougher terms concerning Russian energy supplies, judicial cooperation and Moscow's policies in ex-Soviet countries such as Georgia.
The EU approved a new negotiating mandate on May 27, heeding some of Lithuania's demands.
Solana said the summit would also provide an opportunity to discuss key international and regional issues, including "frozen conflicts" in Georgia and Moldova, the peace process in the Middle East, Iran's controversial nuclear program and ongoing violence in Afghanistan.
The foreign policy chief also said the 'no' vote in Ireland on the Lisbon Treaty, a new version of a common European constitution, would not affect cooperation with Russia. He said the EU was continuing to function on the basis of current treaties while "work has already started on finding a way forward."