His comments came amid fears Russia could cut oil and gas flows in the row over Georgia.

Brown, writing in the Observer, urged the EU to do a "root and branch" review of relations with the Kremlin.

On Saturday President Dmitry Medvedev and Brown spoke by phone as Russia moved to ease tensions with Europe.

Brown wrote in Sunday's Observer newspaper one day ahead of a summit of European heads of state to discuss the South Ossetia crisis.

The conflict in the region began on August 7 when Georgia tried to regain control of South Ossetia by force, which was followed by a Russian counter-attack deep into Georgia.

Brown said: "When Russia has a grievance over an issue such as South Ossetia, it should act multilaterally by consent rather than unilaterally by force."

He went on: "My message to Russia is simple. If you want to be welcome at the top table of organizations such as the G8, OECD and WTO, you must accept that with rights come responsibilities.

"We want Russia to be a good partner in the G8 and other organizations, but it cannot pick and choose which rules to adhere to.

"That is why I will argue tomorrow that Russia should accept Georgia's territorial integrity and international mechanisms for addressing these conflicts, and withdraw troops to their previous positions.

"And, in the light of Russian actions, the EU should review - root and branch - our relationship with Russia."

He added: "We are also reflecting on the NATO response. We must re-evaluate the alliance's relationship with Russia, and intensify our support to Georgia and others who may face Russian aggression."

Brown also said the summit "must add urgency to the work on Europe's energy agenda".

"We must more rapidly build relationships with other producers of oil and gas," Brown said.

The prime minister said he had told Mr Medvedev to expect a "determined response" from European leaders.

During their conversation, Medvedev said Russia was in favor of the deployment to Georgia of additional monitors from the Organization for Security and Co-operation in Europe.

In a separate development, Russian Foreign Minister Sergei Lavrov spoke to his German counterpart Frank-Walter Steinmeier.

They agreed on the need to "put an end to attempts to use the situation surrounding Georgia... to raise tensions in Europe by speculating on non-existent threats concerning other post-Soviet countries", said the Russian foreign ministry.