Officially the one-day summit is focussed on energy issues, with the Europeans seeking to avoid another winter of interrupted supplies of Russian natural gas via Ukraine.
A quarter of the gas consumed throughout the European Union comes from Russia, with most of it transiting Ukraine, which regularly has rows with Russia over bills.
At the summit Prime Minister Fredrik Reinfeldt of Sweden, which holds the rotating EU presidency, will host Russian President Dmitry Medvedev.
They will be hoping to agree on an enhanced 'early warning mechanism' aimed at avoiding any such crises in future, according to a pre-summit note.
However the European side is calling for this system of information exchange to be accompanied by "clear political assurances" from Russia and "third countries concerned" that any further dispute between them will not lead to the taps to Europe being turned off.
Moscow seems not to have heard that request yet.
Russia's ambassador to the EU Vladimir Chizhov said last week that he was unaware of a call for such guarantees, which he said would in any case be impossible to provide.
"We are living in a changing world. Giving guarantees on issues dependent on third countries is not something responsible to do," he said, referring to Ukraine.
Russia would prefer the European Union to aid Kiev financially to pay its gas bills and avoid any more problems.
Agreement will have to be reached despite the strained ties between Moscow and Stockholm.
Last year Sweden and Poland championed the setting up of an Eastern Partnership for the EU with six nations which Russia still considers to be within its sphere of influence: Armenia, Azerbaijan, Belarus, Georgia, Moldova and Ukraine.
Sweden's foreign minister Carl Bildt has also upset Moscow with comments over its human rights record and its brief 2008 war in Georgia.
As a sign of the tensions, the Russians had appeared set at one stage to refuse to attend any summit in Stockholm, according to Swedish sources, preferring the more neutral Brussels.
Moscow still bears a grudge against Bildt over his criticism in August 2008 when he compared Russia's action in Georgia with Hitler's invasion of central Europe.
"We have reason to remember how Hitler used this very doctrine little more than half a century ago to undermine and attack substantial parts of central Europe," Bildt had said, provoking fury in Moscow.
Those comments "were not very helpful" for bilateral relations between Russia and Sweden or "for the atmospherics of the Russia-EU dialogue during the Swedish (EU) presidency," Chizhov said on Friday.
"I hope we'll have constructive discussions rather than a heated exchange of criticism," during the summit, he added.
He may be disappointed, as the Swedes have said they want to push the human rights issue on Wednesday.
"We welcome president Medvedev's comments on democracy and human rights but this has to be followed up with clear deeds, the situation of human rights in Russia is of great concern," Sweden's European affairs minister Cecilia Malmström said recently.
"We'd like to highlight recent events in north Caucasus where we've seen violence against human rights defenders, repression of minorities... also in Russia," she said.
The European side also intends to bring up recent Russian measures deemed protectionist and to see clarification on Russia's formation of a customs union with Kazakhstan and Belarus, which could complicate EU-Russia negotiations on a reinforced partnership deal.
Underlining that there are business as well as political issues in play, the BusinessEurope federation wrote to EU trade commissioner Catherine Ashton last week saying its members were "particularly worried" at Russia's move.
by Yacine Le Forestier/AFP