A Cheney spokeswoman said the vice president told Georgian President Mikheil Saakashvili that Russia's actions "must not go unanswered," CNN reported Monday.
Violence has continued to rage between the two countries since last week when Georgia launched an operation to crack down on separatists in the province of South Ossetia.
Russia responded with an operation Georgia said was aimed at taking control of the region, including a key pipeline that carries Asian oil to Black Sea ports. Russia said it was sending troops to protect peacekeepers in the breakaway province that abuts Russia.
Georgia withdrew its forces Sunday and offered a cease-fire but Russia refused.
Two senior Bush administration officials have told CNN that the United States has sent an envoy to the region to help with mediation aimed at achieving a halt in hostilities.
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