The Foreign Secretary said he was visiting Kiev in a bid to assemble the "widest possible coalition against Russian aggression".
Russia's president Dmitri Medvedev was yesterday accused of "inflaming" the crisis by insisting that South Ossetia and Abkhazia should be independent.
Mr Medvedev told a news agency: "We are not afraid of anything, including the prospect of a new Cold War.
"But we don't want it and in this situation everything depends on the position of our partners."
He said the West would have to "understand the reason behind" the decision to recognise the regions if it wanted to preserve good relations with Russia.
Mr Miliband said Russia's recognition of the two regions was "unjustifiable and unacceptable" and further inflamed an already tense situation in the region.
"It will also not work," he said in a statement yesterday. "It is contrary to the principles of the peace agreement, which Russia recently agreed, and to recent Russian statements.
"It takes no account of the views of the hundreds of thousands of Georgians and others who have been forced to abandon their homes in the two territories."
The Foreign Secretary was backed by Western leaders including US President George Bush and German Chancellor Angela Merkel.
Mr Bush condemned Mr Medvedev's decision as "irresponsible" and called the move "inconsistent" with UN Security Council resolutions and the French-brokered ceasefire plan.
"Russia's action only exacerbates tensions and complicates diplomatic negotiations," Mr Bush said.
Ms Merkel condemned Russia's decision as "absolutely not acceptable," but said Europe must still keep channels of communication open with Moscow.
French Foreign Ministry spokesman Eric Chevallier said the Russian decision was "regrettable, and we reaffirm our attachment to Georgia's territorial integrity".
France, which currently holds the EU presidency, has called an emergency meeting of EU leaders on Monday to review the relationship between Russia and Europe.
Mr Medvedev has warned that he was considering halting co-operation with Nato altogether, amid the fallout from the one-sided military confrontation between Russia and Georgia earlier this month.
Yesterday Russia cancelled a visit by Nato's secretary-general, and it has complained that the alliance is bolstering its military presence in the Black Sea.
And in a move that is likely to increase tensions even further, Mr Medvedev later warned that his country may respond to a US missile shield in Europe through military means.
Mr Medvedev said the deployment of an anti-missile system close to Russian borders "will, of course, create additional tensions".
He said: "We will have to react somehow, to react, of course, in a military way."
In a speech to students in the Ukrainian capital, Kiev, Mr Miliband said that the sight of Russian tanks in Georgia had come as a "rude awakening".
He accused Russian President Dmitry Medvedev of trying to "redraw the map" of the Caucasus through his unilateral recognition of the breakaway provinces of South Ossetia and Abkhazia.
"The Russian President says he is not afraid of a new Cold War. We don't want one. He has a big responsibility not to start one," Mr Miliband said.
Mr Miliband said that he had come to the Ukraine to demonstrate his support for the former Soviet republic, seen by some observers as the next possible target of Russian aggression.
Like Georgia, the pro-Western government in Kiev wants to join Nato and the European Union - moves firmly opposed by Moscow.
"I want to re-affirm the commitment of the United Kingdom to support the democratic choices of the Ukrainian people," Mr Miliband said.
"My visit is designed to send a simple message: we have not forgotten our commitments to you. Nor shall we do so."
The Foreign Secretary said that events in Georgia had ended the period of post-Cold War calm in Europe.
"The Georgia crisis has provided a rude awakening. The sight of Russian tanks in a neighbouring country on the 40th anniversary of the crushing of the Prague Spring has shown that the temptations of power politics remain," he said.
"The old sores and divisions fester. And Russia is not yet reconciled to the new map of this region. Yesterday's unilateral attempt to redraw the map marks a moment of real significance.
"It is not just the end of the post-Cold War period of growing geopolitical calm in and around Europe. It is also the moment when countries are required to set out where they stand on the significant issues of nationhood and international law."
Mr Miliband said the West would not allow the Kremlin to prevent countries like Georgia and Ukraine joining Nato.
"In Nato, we will stand by our commitments to existing members, and there will be renewed determination that there should be no Russian veto on the future direction of Nato," he said.
While Russia had demonstrated its undoubted military might in Georgia, he made clear that there would be a price to pay politically for its actions.
"Today Russia is more isolated, less trusted and less respected than two weeks ago. It has made military gains in the short term. But over time it will feel the economic and political losses," he said.
"If she truly wants respect and influence, and the benefits which flow from it, then Russia needs to change course."
However he rejected calls for the international isolation of Russia, and urged instead a new policy of "hard-headed" engagement with Moscow.
"Isolation is not feasible - Russia is too enmeshed in the world economy," he said.
"It would be counter-productive - its economic integration is the best discipline on its politics. It would only strengthen the sense of victimhood that is the fuel for intolerant nationalism."
However he said Britain and its Western allies needed to "rebalance" their energy relationship with Moscow so that in future they would be less dependent on Russia.
Mr Miliband dismissed Prime Minister Vladimir Putin's assertion that the collapse of the old Soviet Union had been "greatest geopolitical catastrophe" of the 20th century.
"It will only be a tragedy for Russia if it spends the next 20 years believing it to be the case," he said.
He insisted that there had been no "stab in the back" by the West, and that Nato and the EU had in fact tried to engage with Russia.
"These are actions that seek to promote prosperity and respect for Russia. But they have recently been met with scorn," he said.
The Foreign Secretary said Russia needed to respect the independence of former Soviet republics like Ukraine and Georgia in a partnership of equals, "not the relationship of master and servant".
"Over Georgia, Russia has moved from support for territorial integrity to breaking up the country in three weeks and relied entirely on military force to do so," he said.
"In between it signed a ceasefire agreement which included international mediation as the way forward. If her word is not her bond then she will not be trusted by anyone."
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