Barroso said: "I particularly welcome President Medvedev's recent comments about strengthening the rule of law and working together as responsible members of the international community."
A relaxed, smiling Medvedev, hailed the "sincere, neighbourly" mood at the meeting.
The existing ten-year co-operation agreement between the EU and Russia was signed in 1997.
It has been automatically renewed pending the delays on reaching a new one, but the old deal has lost much of its meaning thanks to Russia's new oil and gas wealth and more assertive foreign policy stance.
The EU is being represented by Barroso, Janez Jansa, the Slovenian prime minister, whose country currently holds the EU's rotating presidency, and Javier Solana, the EU foreign policy chief.
Energy security topped the summit's agenda, with the EU wanting Moscow to open its vast energy sector to investors, but the Kremlin firmly intends to maintain its control over Russia's oil and gas riches and energy pipelines.
Meanwhile, Moscow has pushed for more opportunities for its companies to invest in oil and gas distribution assets in Europe to diversify its energy business.
"Russia remains a key energy supplier for the EU, the EU will remain Russia's most important export market,'' Barroso said.
"For both of us, as producers and consumers, energy security is paramount. In this era of high energy prices this is a message our citizens understand only too well."
Peter Mandelson, the bloc's trade chief, said energy security could only be guaranteed if Russia joins the World Trade Organisation (WTO).
He said a wide-ranging economic treaty, within the framework of the new agreement, could not be completed while Russia remains unbound by WTO rules.
Russia, the only major country still outside the WTO, still faces major barriers to membership even after 14 years of negotiations to join the 152-member body, which sets the rules on global trade.
Benita Ferrero-Waldner, the EU external relations commissioner, said on Friday that the bloc wanted "to insert principles of transparency and non-discrimination" into the economic relationship".
The summit gives the EU a chance to test the intentions of Medvedev, who was inaugurated as president in early May.
While Vladimir Putin, his predecessor and mentor, rolled back many post-Soviet democratic reforms during his eight-year tenure, Medvedev has vowed to protect the rule of law, media freedom and human rights.
Skeptics in Russia and the West say Medvedev's pledges are no more than rhetoric and expect him to follow the course of his predecessor, who retains considerable power as Russia's prime minister.
The EU wants Russia to commit to introducing democratic reforms and preserving human rights as part of the new "strategic partnership'' agreement it hopes to have in force by July 2009.
"These subjects will always be on the agenda," Ferrero-Waldner said.
Russia, which has bristled at Western criticism of its democracy record, has in turn urged the EU to pay more attention to what it calls abuse of ethnic-Russian rights in the ex-Soviet Baltic nations, which are now EU members.