Gordon Brown's comments came ahead of a European summit
Prime minister Gordon Brown has said Nato and the EU must reassess their relations with the Kremlin to prevent further "Russian aggression".
His comments came amid fears Russia could cut oil and gas flows in the row over Georgia.
Mr Brown, in the Observer, urged the EU to conduct a "root and branch" review of relations with the Kremlin.
On Saturday President Dmitry Medvedev and Mr Brown spoke by phone as Russia moved to ease tensions with Europe.
Mr Brown wrote the article one day ahead of a summit of European heads of state to discuss the South Ossetia crisis.
The conflict in the region began on 7 August when Georgia tried to regain control of the breakaway region of South Ossetia by force, which was followed by a Russian counter-attack deep into Georgia.
Mr 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 said that if Russia wanted to be welcome at the top table of organisations such as the G8, Organisation for Economic Cooperation and Development (OECD) and World Trade Organization, it must accept that "with rights come responsibilities".
"We want Russia to be a good partner in the G8 and other organisations, 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."
Mr Brown also said there was a need to "rapidly build relationships with other producers of oil and gas".
The prime minister said he had told Mr Medvedev to expect a "determined response" from European leaders.
Meanwhile, Yuri Fedotov, the Russian ambassador to Britain, warned that "any sanctions will hurt the European Union first of all much more than Russia".
He told the BBC: "Russia is not seeking a cold war. Russia is interested in continuing co-operation, business-to-business relations with European countries, with the EU in general, with important partners in America, in Asia.
HAVE YOUR SAY
The EU doesn't need to re-assess its ties with Russia, but instead re-assess its ties with the US
Melvyn Lawes, Brighton
"But if our partners would prefer to chose another option, of course Russia will reply, will react."
Shadow foreign secretary William Hague said European states should resist a rush to sanctions and instead exert long-term pressure.
"It is very important for the EU now to reassess its relationship with Russia and send a very clear message," he told Sky News.
"I do not think the measures looked at tomorrow should be cheap or quick. This requires clear and united and patient firmness over a sustained period of time."
Former Liberal Democrat leader, Sir Menzies Campbell, said it could be dangerous to isolate Russia.
"I think we've got to make clear our displeasure about the way in which Russia has acted outrageously," he told the BBC.
"But if by doing so, in a particular way and with particular language, we drive Russia into isolation, then sulking Russia, in isolation, will be even more difficult to deal with.
"And that's why when people talk about expulsion from the G8 and things of that kind, I think they've got to understand what the possible consequences of that would be to the Russian government's attitude."
Meanwhile, Foreign Secretary David Miliband, writing in the Mail on Sunday, said there is no excuse for the violation of international law.
"Russia has become the aggressor - it has gone from claiming to defend Russian passport holders in regions of Georgia to seeking the break-up of the state, showing disregard for the principles of modern international relations," he said.
During his conversation with Mr Brown, Mr Medvedev said Russia was in favour of the deployment to Georgia of additional monitors from the Organisation for Security and Co-operation in Europe.
Georgia has cut diplomatic ties with Russia after Moscow recognised the independence of the breakaway regions of South Ossetia and Abkhazia.