Bush put the crisis at the top of his agenda as he returned from the Olympic Games in Beijing.
In a Rose Garden statement, he said there appeared to be an attempt by Russia to unseat Georgia's pro-Western president, Mikhail Saakashvili.
He demanded an immediate cease-fire, the withdrawal of Russian troops from the conflict zone and a return to the status quo as of Aug. 6.
Russia has ignored calls for a truce and has responded with overwhelming military force. It appeared Bush had little leverage to win Moscow's compliance.
Bush said the military crackdown has "substantially damaged Russia's standing in the world. And these actions jeopardize Russia's relations with the United States and Europe. It is time for Russia to be true to its word and to act to end this crisis."
On Monday, Russian armored vehicles rolled deep into western Georgia, quickly taking control of several towns and a military base and slicing open a damaging second front in Russia's battle with Georgia. Other Russian forces captured the key central city of Gori.
Fighting also raged Monday around Tskhinvali, the capital of the separatist province of South Ossetia. Swarms of Russian planes launched new raids across Georgia, with at least one sending screaming civilians running for cover.
The invasions of Gori and the towns of Senaki, Zugdidi and Kurga came despite a top Russian general's claim earlier Monday that Russia had no plans to enter Georgian territory. By taking Gori, which sits on Georgia's only east-west highway, Russia has the potential to effectively cut the country in half.
Alex Rossi, of CBS News partner Sky News, told CBS' The Early Show that the city of Gori was bombed early Friday, and that some civilian locations were hit.
Rossi said fighting around the capital city of South Ossetia had largely quieted Friday and that Russian troops appeared to be fully in control of the breakaway region, leaving Georgian forces to retreat and take up defensive positions.
Security Council head Alexander Lomaia said Monday it was not immediately clear if Russian forces would try to advance on Tbilisi, the Georgian capital. Georgia sought at urgent meeting of the U.N. Security Counil in New York - the fifth meeting on the subject in as many days.
Also, the U.S. State Department said it has evacuated more than 170 U.S. citizens from Georgia as the conflict over separatist areas there intensifies between Georgia and Russia.
A spokesman said Monday that two convoys carrying about 170 private U.S. citizens along with an undetermined number of family members of American diplomats based in Georgia have left Tbilisi on their way by road to neighboring Armenia.
The two-front battlefield was a major escalation in the conflict that blew up late Thursday after a Georgian offensive to regain control of the separatist province of South Ossetia. Even as Georgian President Mikhail Saakashvili signed a cease-fire pledge Monday with EU mediators, Russia flexed its military muscle and appeared determined to subdue the small U.S. ally that has been pressing for NATO membership.
Russian armored personnel carriers moved into Senaki, a town 20 miles inland from Georgia's Black Sea port of Poti, Lomaia said. Russian forces also moved into Zugdidi, near Abkhazia, and seized police stations, while their Abkhazian allies took control of the nearby village of Kurga, according to witnesses and Georgian officials.
In Zugdidi, an AP reporter saw five or six Russian soldiers posted outside an Interior Ministry building. Several tanks and other armored vehicles were moving through the town but the streets were nearly deserted, with shops, restaurants and banks all shut down.
Georgia borders the Black Sea between Turkey and Russia and was ruled by Moscow for most of the two centuries preceding the 1991 breakup of the Soviet Union. Both provinces of South Ossetia and Abkhazia have run their own affairs without international recognition since fighting to split from Georgia in the early 1990s - and both have close ties with Moscow.
Georgia began an offensive to regain control over South Ossetia late Thursday with heavy shelling and air strikes that ravaged South Ossetia's provincial capital of Tskhinvali.
"There is no question that Georgia started this conflict with an offensive against the separatists of South Ossetia because its entry to NATO required a resolution to the problem, but the disproportiate and continuing military attacks by Russia appears to have united the European Union and the U.S. in a call for the removal of Russian troops," said CBS News foreign affairs analyst Pamela Falk.
"The fighting has now created a major refugee crisis that is spilling over to regional states," Falk added, "and a political crisis with fears that Russia is trying to overthrow the democratically-elected, pro-Western government of Georgia."
The Russia response was swift and overpowering - thousands of troops that shelled the Georgians until they fled Tskhinvali on Sunday, and four days of bombing raids across Georgia.