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In an article in Sunday's Observer newspaper, Brown said he had spoken to Russian President Dmitry Medvedev and told him to expect a determined response when European leaders meet to discuss the Georgia crisis on Monday.
The EU meeting in Brussels will debate the bloc's response to Russia's military intervention and its decision to recognize South Ossetia and Georgia's other breakaway region, Abkhazia, as independent states.
The Russian incursion has raised fears in the West that an important oil pipeline from the Caspian Sea to the Turkish Mediterranean coast via Georgia could come under Russian control.
Brown said he would press European leaders to increase funding to allow EU nations to source energy from the Caspian, reducing dependency on Russia.
"No nation can be allowed to exert an energy stranglehold over Europe," the Observer quoted Brown as saying in a front-page story.
In his article, Brown said: "Without urgent action, we risk sleepwalking into an energy dependence on less stable or reliable partners."
Russia must play by the rules if it wants to enjoy the benefits of bodies such as the Group of Eight, the Organization for Economic Cooperation and Development and the World Trade Organization, Brown said.
"And, in the light of Russian actions, the EU should review -- root and branch -- our relationship with Russia," he said.
It may be necessary to exclude Russia when the other G8 nations meet, and NATO's relationship with Moscow must be re-evaluated, Brown said, pledging intensified Western support for Georgia and "others who may face Russian aggression".