Mr Miliband said Russia's declaration had inflamed an already tense situation
UK Foreign Secretary David Miliband has called on the EU and Nato to initiate "hard-headed engagement" with Russia in response to its actions in Georgia.
In a speech in Ukraine's capital, Kiev, he urged them to bolster their allies, rebalance the energy relationship with Russia and defend international law.
Russia recognised the independence of Georgia's two breakaway regions, South Ossetia and Abkhazia, on Tuesday.
Moscow's fellow G8 members have condemned its actions in Georgia.
"We, the foreign ministers of Canada, France, Germany, Italy, Japan, the United States and the United Kingdom, condemn the action of our fellow G8 member," the group of seven of the world's leading industrialised nations said in a joint statement.
"We deplore Russia's excessive use of military force in Georgia and its continued occupation of parts of Georgia."
Ukraine's President Victor Yushchenko has said his country is a hostage in a war waged by Russia against countries in the old Soviet bloc.
Russia was, is and will continue to be the last country in the world that would want a repeat of the Cold War
He told Mr Miliband that the brief conflict between Georgia and Russia earlier this month had exposed serious weaknesses in the powers of the UN and other international bodies.
He called for Ukraine's defences to be strengthened and said his country would consider increasing the amount of money Russia pays for the lease of the port of Sevastopol, where it stations its Black Sea Fleet.
"When we allow someone to ignore the fundamental right of territorial integrity, we put into doubt the independence or existence of any country, any nation," he said.
Fighting between Russia and Georgia began on 7 August after the Georgian military tried to retake its Russian-backed breakaway province of South Ossetia by force.
Russian forces subsequently launched a counter-attack and the conflict ended with the ejection of Georgian troops from both South Ossetia and Abkhazia and an EU-brokered ceasefire.
After holding talks with President Yushchenko, Mr Miliband told a group of students in Kiev that the Georgia crisis had "provided a rude awakening".
David Miliband said Russia must not start a new Cold War
Mr Miliband said Moscow's "unilateral attempt to redraw the map marks a moment of real significance".
Russian President Dimitry Medvedev, he said, had a "big responsibility not to start" a new Cold War.
The foreign secretary said the response of the EU and Nato to such "aggression" should be one of "hard-headed engagement".
"That means bolstering our allies, rebalancing the energy relationship with Russia, defending the rules of international institutions, and renewing efforts to tackle 'unresolved conflicts'," he explained.
Mr Miliband again rejected calls for Russia to be expelled from the G8, but did suggest the EU and Nato needed to review relations with it.
He also reiterated the British government's support for Ukraine's application for full Nato membership.
The Russian government later responded to Mr Miliband's criticism by saying Moscow saw no threat of a new Cold War.
A spokesman for Prime Minister Vladimir Putin said Russia had been taking "measures of precaution" against Nato warships in the Black Sea, but hoped to avoid confrontation.
"I wouldn't agree that we really have a threat of a new Cold War. Russia was, is and will continue to be the last country in the world that would want a repeat of the Cold War," Dmitry Peskov said.
China meanwhile addressed the crisis for the first time by expressing "concern" about developments in South Ossetia and Abkhazia and urging dialogue.
The comments came as Chinese President Hu Jintao met President Medvedev in Tajikistan ahead of a regional summit.
In other developments
Georgia moved to reduce its diplomatic presence in Moscow, confirming its ambassador would not return
German Chancellor Angela Merkel said the continued presence of Russian forces in Georgia proper was a grave ceasefire violation. She also agreed to send up to 15 military observers to Georgia as part of an OSCE mission
Russian Foreign Minister Sergei Lavrov said Moscow would support the presence of more international monitors in the buffer zones
French President Nicolas Sarkozy described Moscow's decision as an unacceptable attempt to change borders, and said any settlement had to be based on international law, dialogue and respect for Georgia's territorial integrity
French Foreign Minister Bernard Kouchner called Russia an "international outlaw" and said the real worry was not a new Cold War but a "hot" one, suggesting that another Russian objective might now be Ukraine's mainly Russian-speaking territory of Crimea.
On Tuesday, Mr Medvedev said Moscow had been obliged to recognise the independence of South Ossetia and Abkhazia following the "genocide" started by Georgian President Mikhail Saakashvili in South Ossetia in August.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.