WASHINGTON — The sudden outbreak of war in Georgia presents a foreign policy challenge both for the Bush administration and the presidential candidates as they grapple with an emboldened Russia intent on re-asserting its power on the world stage.

Fighting escalated dramatically over the weekend as Russian forces advanced beyond the disputed separatist region of South Ossetia and into Georgian territory, according to news reports from the region. The Georgian president, Mikheil Saakashvili, said he had withdrawn troops from South Ossetia and was observing a cease-fire, but Russian officials disputed that claim, the Associated Press reported. The Russian military reportedly sank a Georgian boat and twice bombed an area near the nation’s airport; claims of casualties from the conflict, which began late last week, numbered in the thousands.

Bush administration officials urged an immediate halt to the violence in the Caucasus and warned that Russia’s aggression risked damaging its relationship with America.

President Bush, in an interview with NBC, said yesterday that the violence is ” unacceptable.”

“I’ve expressed my grave concern about the disproportionate response of Russia and that we strongly condemn the bombing outside of South Ossetia,” Mr. Bush told NBC.

Vice President Cheney spoke to Mr. Saakashvili yesterday afternoon and “expressed 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,” Mr. Cheney’s spokeswoman, Lee Ann McBride, said according to the AP.

Mr. Cheney told Mr. 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,” Ms. McBride said.

Russian officials said its move into South Ossetia was a response to Georgian attacks on its peacekeepers in the disputed territory, but analysts said the large-scale military incursion represented at the least a grossly disproportionate retaliation by the Kremlin and may have even been a deliberate and long-planned provocation by Moscow aiming to demonstrate its dominance in the region.

Russia has long been close to the separatists opposed to Georgian rule in the enclaves of Abkhazia and South Ossetia, and it has staunchly resisted the attempt by Georgia, a former Soviet republic and an American ally, to gain entry into the North Atlantic Treaty Organization. A major oil pipeline originating in the Caspian Sea runs through Georgia to Turkey, adding to the geopolitical importance of the region.

The war is reverberating through the presidential campaign in America, with both candidates issuing multiple statements over the weekend reacting to the crisis. The political fallout may favor the presumptive Republican nominee, Senator McCain, who has viewed Russia skeptically and has mocked Mr. Bush’s once-close bond with its leader, Vladimir Putin. During a foreign policy speech in March, Mr. McCain called for ousting Russia from the G-8. He has also served as chairman of the International Republican Institute, which has long voiced support for Georgia in its conflict with Russia.

The Arizona senator immediately blamed Russia for the outbreak in violence on Friday, issuing a statement that called on the Kremlin to “unconditionally cease its military operations and withdraw all forces from sovereign Georgian territory.” By contrast, the initial one-paragraph statement from the Obama campaign contained no criticism of Russia and put the onus on both nations “to show restraint and to avoid an escalation to full-scale war.”

A day later, Mr. Obama issued a much lengthier statement that significantly ramped up the rhetoric toward Russia. After disclosing that he had spoken directly with the secretary of state, Condoleezza Rice, and with Mr. Saakashvili of Georgia, he said: “I condemn Russia’s aggressive actions and reiterate my call for an immediate ceasefire. Russia must stop its bombing campaign, cease flights of Russian aircraft in Georgian airspace, and withdraw its ground forces from Georgia.”

Mr. McCain also released a second statement and noted that he had long warned of Russia’s hostile behavior toward its neighbors.

“Unfortunately, we have seen in recent days Russia demonstrate that these concerns were well-founded,” he said.

For Mr. McCain, the crisis signals another opportunity for him to swing the presidential debate to the area where he is most comfortable — foreign policy — and away from the economy, a topic that has dominated the campaign but one that he has acknowledged is not his strength. McCain surrogates underscored the point in appearances yesterday on the Sunday morning talk shows. “I think this is another example during these uncertain times, where we need experienced leadership,” Governor Jindal of Louisiana said on ABC’s “This Week.” “We need somebody like Senator McCain who will take a stronger view, a more experienced view, when it comes to international security and protecting America’s interest.”

The Republican’s campaign also attacked Mr. Obama’s camp for making an issue of lobbying work conducted for the Georgian government by a top McCain foreign policy adviser, Randy Scheunemann. A McCain spokesman, Tucker Bounds, said the criticism of Mr. Scheunemann was “disgraceful” and “bizarrely in sync with the Kremlin.”

Speaking yesterday on Mr. Obama’s behalf, Governor Richardson of New Mexico said America had lost leverage with Russia because the Bush administration had allowed relations to deteriorate.

“The problem, though, is that we don’t have the kind of influence and strength in our relationship with Russia to persuade them,” the former United Nations ambassador said on “This Week.” “This has been one of the failures of the Bush administration.”

A Russia scholar at the conservative Heritage Foundation who has informally advised the McCain campaign, Ariel Cohen, criticized what he characterized as a weak response to the crisis from Mr. Obama. “The Obama campaign is caught like a deer in headlights with platitudes of diplomacy that can only encourage further Russian aggression,” he said. Mr. Cohen said Russia’s incursion was likely planned for months and that it was intended to demonstrate its hegemony over Eastern Europe and to push Mr. Saakashvili from power in Georgia.

A senior fellow at the Atlantic Council of the United States, Adrian Karatnycky, said it was unclear whether Russia had long plotted the move but that its breach of the Georgian border marked a significant shift in its policy toward disputed territories such as South Ossetia and Abkhazia. “Russia has now crossed a very dangerous line,” he said.

Mr. Karatnycky, a former president of Freedom House, said that despite Mr. McCain’s harsh rhetoric toward Russia, the difference in policy between him and Mr. Obama would likely be minimal. “I don’t see a big gap in the read on Russia,” he said, noting that the Democrat had also urged a tougher line on the Kremlin.

But he did take issue the criticism of the Bush administration advanced by Mr. Richardson, with whom he had worked closely at Freedom House. “I just don’t think being nice to Putin would have changed one iota,” he said.