Mr Brown says there is a pressing need for fighting to end.
UK Prime Minister Gordon Brown says there is "no justification" for Russia's military action in Georgia.
He said the intervention "threatens the stability of the entire region and risks a humanitarian catastrophe".
"There is a clear responsibility on the Russian government to bring this conflict quickly to an end," he said.
Tory leader David Cameron branded Russia a "dangerous bully" and urged the international community to stand up and condemn its action in Georgia.
He also called for Georgia's membership of Nato to be "speeded up".
Mr Cameron told the BBC: "The only language that bullies understand is when someone stands up to them."
UK nationals have been advised not to travel to Georgia and those in the country have been urged to leave.
As fighting over the disputed region of South Ossetia threatens to spread more widely, Mr Brown warned there was "an immediate and pressing need to end the fighting and disengage all military forces".
He said the Georgian government had offered a ceasefire and he urged "the Russians to reciprocate without delay".
"Continued aggression against Georgia - and especially an escalation of the conflict beyond South Ossetia - will only serve to damage Russia's international reputation and its relations with countries across the globe," he said.
Mr Brown has held discussions with France's President Nicolas Sarkozy and UN Secretary General Ban Ki Moon in recent days.
Foreign Secretary David Miliband has also held talks with G7 and EU foreign ministers.
"We are committed to working with those partners in the EU, UN, OSCE [Organisation for Security and Cooperation in Europe] and G7 to ensure a peaceful and speedy resolution to this crisis which maintains Georgia's territorial and political integrity," Mr Brown added.
Earlier, Mr Cameron warned that there were "very, very worrying consequences" if Europe failed to speak with one voice that what Russia is doing "is wrong".
"What Russia has done here is used massive and disproportionate force. It's breached international law and it has violated Georgia's territorial integrity," he told BBC Radio 4's The World at One.
"It has acted as a massive and dangerous bully and we can't allow this to go ahead without it being challenged."
Mr Cameron conceded that Georgia's decision to send troops into South Ossetia "was a bad strategy", but he said there could be implications for Baltic states that still identify with Russia if nations fail to speak out.
Amnesty International has called on Georgia and Russia to provide safe passage to people fleeing from the conflict and allow unimpeded access to humanitarian relief to those in affected areas.
The calls for an immediate ceasefire were echoed by the British ambassador to Georgia, Denis Keefe. who said the objective of the Russians was unclear.
"They have gone well beyond the conflict zones which they used as the grounds for their action in the first place," he told BBC Radio 4's Today programme.
"They have bombed in different areas in the country. They have sent their troops into different areas of the country.
"The result is a real and pressing need for a ceasefire to disengage military forces.
"I think the question of what the Russians are trying to achieve is impossible to answer from Tbilisi at the moment. What is clear here is that we need a ceasefire and we need it now."