Foreign Secretary David Miliband visited Georgia as Nato stepped up pressure on Russia to withdraw its forces from the former Soviet state.
Nato warned Moscow that it "cannot continue with business as usual" while Russian troops remain in Georgia.
Mr Miliband said Russia "violated international law" by sending troops into Georgia after violence erupted in breakaway province South Ossetia.
Speaking at a joint press conference with Georgian President Mikheil Saakashvili in Tbilisi, the Foreign Secretary said Russia was not living up to the commitment it had made in the ceasefire.
The British Government and the British people stood in solidarity with Georgia, he said.
"The British policy is founded on very clear foundations, that the rule of force does not replace the rule of law, and the territorial integrity of sovereign nations is to be respected," he said.
"On several counts Russian behaviour over the last 10 days has violated those principles.
"It was striking to hear all Nato members talking about the need to ensure that aggression does not pay."
Russia needed to realise that the world had moved "decisively beyond the Soviet era", he said, and "force is not a basis to redraw the map" of surrounding nations.
The Foreign Secretary added: "Russia wants to be a respected international player but it can only be so if it lives up to its responsibilities."
