Article published on the 2008-08-27 Latest update 2008-08-27 14:59 TU
Referring to a news agency interview in which Medvedev declared that Russia is "not afraid of anything, including the prospect of a new Cold War", Milliband declared, "He has a big responsibility not to start one."
Earlier the British minister said that his Ukraine visit aims to build the "widest possible coalition against Russian aggression".
Ukrainian President Viktor Yuschcenko condemned Medvedev's recognition of South Ossetia and Abkhazia as independent and declared that it threatened security in other countries which were previously part of the Soviet Union.
French Foreign Affairs Minister Bernard Kouchner told Europe 1 radio that the Russian move is against international law and speculated that it might now have its sights set on "the Crimea, Ukraine and Moldova".
British analyst Paul Rogers says that the EU faces problems in a confrontation with Russia.
"The difficulty for the EU is that there is a lot of concern about this crisis getting even worse, particularly if it was to involve the Crimea and Ukraine," he told RFI. "Also you have this very strong EU dependence, particularly with the new states, on Russian oil and gas."
Like Georgia, Ukraine's president would like it to join Nato. Yushchencko says that his country may raise the rent on Russia's Black Sea fllet base at the Ukrainian port of Sevastopol, a move which Moscow says would break a 1997 agreement.
Russian generals say that its navy has been ordered to monitor the growing number of Nato naval ships in the Black Sea.
Georgia has now said that it will pull two of its diplomats out of its Moscow embassy, further reducing its representation there after recalling its ambassador in April over Russia's establishment of formal ties with the rebel governments in Abkhazia and South Ossetia.
Politicians in Tbilisi are preparing attempts to have Russia expelled from several international organisations.