U.S. Vice President Dick Cheney has called Russia's actions in Georgia an unjustified assault, and has pledged to ensure that country's territorial integrity.
The vice president made his comments while addressing a meeting of veterans in the western U.S. state of Arizona.
Earlier, French President Nicolas Sarkozy called on Russia to comply immediately with the international cease-fire agreement requiring the withdrawal of Russian troops from Georgia. Russia signed the deal, but its forces remain in key positions inside Georgia, prompting a flood of Western criticism.
Mr. Sarkozy also sharply criticized Russia's decision to unilaterally recognize the independence of the breakaway Georgian territories of South Ossetia and Abkhazia.
In Kyiv, British Foreign Minister David Miliband rejected Moscow's recognition of the two regions. Speaking at a joint news conference with Ukrainian President Viktor Yushchenko, Mr. Miliband stressed the importance of respect for the sovereignty, integrity and democracy of nation states.
He also said Russia has "a big responsibility" not to start a new Cold War.
Earlier, Mr. Yushchenko called Russia's decision to recognize the independence of South Ossetia and Abkhazia unacceptable.
French Foreign Minister Bernard Kouchner and European Union Enlargement Commissioner Olli Rehn have warned that Moscow may be eyeing Ukraine and Moldova, in a push to strengthen Moscow's influence in former Soviet-ruled territories.
Meanwhile, Russian President Dmitri Medvedev briefed Chinese President Hu Jintao about Russia's views on the Georgian crisis. The two met in the Tajik capital, Dushanbe, the site of a regional summit of the Shanghai Cooperation Organization.
Separately, a U.S. Coast Guard cutter carrying humanitarian aid to victims of the Russian incursion arrived Wednesday in the Georgian port of Batumi.
U.S. authorities say a U.S. Navy supply vessel will bring additional humanitarian aid to Batumi in coming days.
Russia sent several naval vessels to the Abkhazian port of Sukhumi, as senior Russian military officials questioned the U.S. use of military vessels to deliver the aid.
Georgian troops moved into South Ossetia on August 7, in a push to regain control of the rebellious territory. The move triggered a massive Russian response, with Moscow sending in tanks and thousands of troops, saying it had to protect Russian citizens in the region.
Some information for this report was provided by Reuters.