Both candidates said Europe and other nations must be united against Russia's widening assault against Georgia, U.S.'s closest ally among the democratizing former Soviet republics. And they said NATO should reconsider its decision to withhold a "membership action plan" for Georgia.
That decision "might have been viewed as a green light by Russia for its attacks on Georgia," McCain, a Republican senator from Arizona, said.
Speaking to reporters in Pennsylvania, McCain said Russia appears intent on toppling the Georgian government rather than simply restoring the status quo in the pro-Moscow province of South Ossetia, which Georgia is trying to keep from breaking away.
"NATO's North Atlantic Council should convene in emergency session to demand a ceasefire and begin discussions on both the deployment of an international peacekeeping force to South Ossetia and the implications for NATO's future relationship with Russia," McCain said.
He said the United States "should coordinate with our partners in Germany, France and Britain, to seek an emergency meeting of the G-7 foreign ministers to discuss the current crisis."
"We must remind Russia's leaders that the benefits they enjoy from being part of the civilized world require their respect for the values, stability and peace of that world," McCain said.
(Read More About McCain's Statement In CBSNews.com's From The Road Blog)
Obama, a Democratic senator from Illinois, also urged a multinational response but added that U.N. Security Council should play a major role in helping end the crisis. He said the Security Council should pass a resolution calling for an immediate end to the violence, and urged a U.N. mediator to join French and Finnish foreign ministers in Georgia to try to end the fighting.
"The U.N. must stand up for the sovereignty of its members and peace in the world," Obama told reporters during his weeklong vacation in Hawaii.
Like McCain, Obama warned that Russia's future relationships are at stake. An international forum, he said, should be convened to review Russia's interest in joining the World Trade Organization.
"We want Russia to play its rightful role as a great nation," Obama said. "But with that role comes the responsibility to act as a force for progress in this new century, not regression to the conflicts of the past."