WASHINGTON -LRB- CNN -RRB- -- President Bush condemned the escalated violence between Russia and U.S.-backed Georgia on Sunday , while Vice President Dick Cheney said aggression against Georgia `` must not go unanswered . '' President Bush chats with Russian Prime Minister Vladmir Putin at the start of the Olympic opening ceremonies . `` My administration has been engaged with both sides of this trying to get a ceasefire , '' Bush told NBC 's Bob Costas in an interview in Beijing , China , where the president has attended Olympic events . Bush was filmed speaking to Russian Prime Minister Vladimir Putin during Friday 's opening ceremonies and said Sunday that he `` was firm with Vladimir Putin '' and that `` this violence is unacceptable . '' Violence has continued to rage between Russia and the western ally since Thursday , when Georgia launched an operation to crack down on separatists in South Ossetia territory . Russia said it wanted to protect its peacekeepers already in South Ossetia following ceasefires in years past . But Georgia called it a full-on invasion . And while Russia has accused Georgia of a genocidal plot to cleanse the region of ethnic Ossetians loyal to Russia , Georgia accuses Russia of executing a long-planned war with the aim of taking control of the region -- including a key pipeline that carries Asian oil to Black Sea ports . `` I expressed my grave concern about the disproportionate response of Russia , '' Bush said of his talk with Putin . `` We strongly condemn bombing outside of South Ossetia . '' Putin says he 's concerned about the flood of refugees arriving in Russia from South Ossetia . Russian officials said more than 30,000 refugees have left South Ossetia and crossed into Russia over the past two days , Interfax reported . `` The actions of the Georgian authorities in South Ossetia are a crime , of course , primarily a crime against their own people , '' Putin said , according to Russian news agency Interfax . Meanwhile , Cheney talked to Georgian President Mikheil Saakashvili on Sunday , telling him that Russia 's aggression against Georgia `` must not go unanswered . '' Cheney 's spokeswoman Lea Ann McBride said the vice president spoke to Saakashvili to express `` the United States ' solidarity with the Georgian people and their democratically elected government in the face of this threat to Georgia 's sovereignty and territorial integrity . '' Georgia withdrew its forces Sunday and offered a ceasefire , which Russia refused . `` The vice president told President Saakashvili that Russian aggression must not go unanswered , and that its continuation would have serious consequences for its relations with the United States , as well as the broader international community , '' McBride said . Saakashvili has called on the United States and the world community to stop the `` intervention and invasion of my sovereign country . '' `` I think the U.S. is the most powerful country in the world , '' he told CNN . `` I think the U.S. has lots of leverage . And I think there are lots of diplomatic means that it could be done through . '' Two senior officials have told CNN the United States sent envoy Matt Bryza to the region to help with mediation .