TBILISI, Georgia — Swarms of Russian jets launched new raids on Georgian territory today and Georgia faced the threat of a second front of fighting as Russia demanded that Georgia disarm troops near the breakaway province of Abkhazia.

While a senior Russian general insisted that Russia has no plans to press further into Georgian territory — its troops are now in two breakaway provinces — the order to disarm carried the threat that Russian-sponsored fighting would spread.

The new air forays into Georgia — even as Georgian President Mikhail Saakashvili on signed a cease-fire pledge — appeared to show Russian determination to subdue the small, America-backed country, which has been pressing for NATO membership. Russia fended off a wave of international calls to observe Georgia’s pleas for a truce, saying it must first be assured of Georgia’s retreat from South Ossetia.

America is campaigning to get Russia to halt its retaliation and American officials have accused Russia of using the fighting to try to overthrow the Georgian government. President Bush, who has encouraged Georgia’s efforts to join NATO, said he spoke with Prime Minister Putin and the Russian president.

“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 said in an interview with NBC Sports.

In turn, Mr. Putin criticized America for airlifting Georgian troops back home from Iraq on Sunday at Georgia’s request.

“It’s a pity that some of our partners instead of helping are in fact trying to get in the way,” Mr. Putin said at a Cabinet meeting. “I mean among other things the United States airlifting Georgia’s military contingent from Iraq effectively into the conflict zone.”

A two-front battlefield would be a major escalation in the conflict, which blew up Friday after a Georgian offensive to regain control of separatist South Ossetia.

Most Georgian troops are near South Ossetia, in the center of the country along its northern border with Russia, which would make it difficult for Georgia to repel an offensive from Abkhazia, in the west along the Black Sea.

International envoys flew into the region late yesterday and the U.N. Security Council met for the fourth time in as many days to try to end the conflict before it spreads throughout the volatile Caucasus.

At Tbilisi, Mr. Saakashvili signed a cease-fire pledge today proposed by the French and Finnish foreign ministers. The EU envoys plan to travel from Tbilisi to Moscow later today to try to persuade Russia to accept it.

Mr. Saakashvili had ordered the halt yesterday after overwhelming Russian firepower blasted his troops out of the South Ossetian capital of Tskhinvali, but Russian officials said they saw no cease-fire on the ground.

At Moscow, President Medvedev said Russia has completed “a large part of efforts to force Georgian authorities to peace in South Ossetia,” a statement that suggests Moscow could accept the proposed cease-fire.

Mr. Saakashvili, however, voiced concern that Russia’s true goal was to undermine his pro-Western government. “It’s all about the independence and democracy of Georgia,” he said during a conference call.

At a U.N. Security Council meeting yesterday, Russia’s ambassador to the United Nations, Vitaly Churkin, acknowledged there were occasions when elected leaders “become an obstacle.”

Mr. Saakashvili said Russia has sent 20,000 troops and 500 tanks into Georgia — with some troops getting within three miles of Gori, located just outside South Ossetia, before being repulsed yesterday.

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 South Ossetia and Abkhazia have run their own affairs without international recognition since fighting to split from Georgia in the early 1990s.

Both separatist provinces have close ties with Moscow, while Georgia has deeply angered Russia by wanting to join NATO.

Georgia began an offensive to regain control over South Ossetia overnight Friday with heavy shelling and air strikes that ravaged the city of Tskhinvali. The Russia response was swift and overpowering — thousands of troops that shelled the Georgians until they fled Tskhinvali yesterday, and air attacks across Georgia, some on facilities far from the site of the fighting.

The Georgian president said Russian warplanes were bombing roads and bridges, destroying radar systems today and targeting Tbilisi’s civilian airport last night. One Russian bombing raid struck the Tbilisi airport area just a half-hour before the EU envoys arrived, he said.

Georgia said another hit Friday near the key Baku-Tbilisi-Ceyhan oil pipeline, which carries Caspian crude to the West. No supply interruptions have been reported and Russia denies targeting the pipeline.

While not addressing reports of the incursion near Gori, Nogovitsyn, the Russian general, said Russia had no intention to move deeper into Georgia. “We aren’t planning any offensive,” he said.

Mr. Saakashvili later drove to the outskirts of Gori, a town where scores of people were killed in an Russian attack Saturday. He was joining French Foreign Minister Bernard Kouchner, who had just completed a tour of the destroyed buildings.

As the Georgian president spoke to reporters next to his SUV, a member of his security team shouted “cover him!” Mr. Saakashvili was torn away by bodyguards and pushed to the ground. They piled extra flak jackets on top of him.

Fearing an air raid, onlookers fled, looking skyward and screaming. No jets were seen or heard.

Mr. Kouchner had left seconds before the panic.

“This a misfortune, this is impossible to support,” Mr. Kouchner said after touring Gori. “That’s why we not only have to denounce this, but we have to work to stop the fight.”

Russia’s Deputy Foreign Minister, Grigory Karasin, said more than 2,000 people had been killed in South Ossetia since Friday, most of them Ossetians with Russian passports. The figures could not be independently confirmed, but refugees who fled the city said hundreds were killed.

Thousands of civilians have fled South Ossetia — many seeking shelter in the neighboring Russian province of North Ossetia.

“The Georgians burned all of our homes,” said one elderly woman, as she sat on a bench under a tree with three other white-haired survivors of the fighting. “The Georgians say it is their land. Where is our land, then?”

General Nogovitsyn said on Russian television today that Russia demanded Georgia disarm police at Zugdidi, a town just outside Abkhazia, but did not say what would happen if they do not.

Abkhazia’s Russian-supported separatist government called out the army and reservists on Sunday and declared it would push Georgian forces out of the northern part of the Kodori Gorge, the only area of Abkhazia still under Georgian control.

A Russian commander said 9,000 additional Russian troops and 350 armored vehicles had arrived in Abkhazia.

General Nogovitsyn also said Russian ships deployed to Georgia’s Black Sea coast sank one of four Georgian patrol boats that came close yesterday — a report rejected by Georgia’s Coast Guard chief, David Golua.

At New York, the U.N. Security Council met for the fourth time yesterday in four days to discuss the crisis. U.S. Ambassador Zalmay Khalilzad accused Moscow of seeking “regime change” in Georgia and resisting attempts to make peace.

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Associated Press writers David Nowak in Gori, Georgia; Douglas Birch in Vladikavkaz, Russia; Jim Heintz, Vladimir Isachenkov and Lynn Berry in Moscow; John Heilprin at the United Nations contributed to this report.