Russia and the EU are each other's biggest trading partner, but political tensions remain high.
Moscow recently accused the 27-member bloc of creating new dividing lines in Europe by offering closer ties to six former Soviet republics.
And Russia's control of gas supplies to Europe remains a bone of contention.
No-one expects any breakthroughs at the summit, the BBC's Richard Galpin in Moscow says.
Perhaps the biggest hope is for an agreement to resume negotiations on a new partnership deal which first began almost a year ago, our correspondent says.
'Russia's greatness'
European Commission chief Jose Manuel Barroso, foreign policy chief Javier Solana and Czech President Vaclav Klaus are leading the EU team in Khabarovsk.
The Russian delegation is headed by President Dmitry Medvedev.
"We need to come back to the financial and economic crisis, we need to talk about the state of affairs in the energy sector and a new security architecture," he said as the meeting opened.
He said earlier that Khabarovsk - 6,000 km (3,700 miles) from Moscow but just 30 km from the Chinese border - had been chosen as the venue for the talks to allow the visitors to "appreciate Russia's greatness".
A year ago - when Mr Medvedev became Russia's new leader - there was hope that relations with the EU might gradually improve, our correspondent says.
Instead, he says, they have got steadily worse.
Relations plummeted after last year's brief war between Russia and Georgia.
Since then there has been another gas dispute between Russia and Ukraine which led to gas supplies to many European countries being cut off for two weeks in mid-winter.
There is also a growing battle over energy pipelines as the EU tries to find alternatives to its growing dependency on Russian gas.
There is also concern in the EU about Russia's recent increase of customs duties on a wide range of European imports, including steel, starch and TV screens - despite its pledge to fight protectionism along with its G20 partners.
