On his first day in office, Russian Prime Minister Vladimir Putin took charge today of putting down an escalating guerrilla conflict in the rebellious southern province of Dagestan and vowed to reestablish order there "in the shortest time."

Putin, appointed by President Boris Yeltsin on Monday, met with Yeltsin, his cabinet and Russian army officials over the crisis and, in televised remarks, used tough language to condemn the Islamic militants who have launched an uprising similar to the one waged three years ago in neighboring Chechnya.

"We are dealing with a mass display of terrorism and violation of law," he said in setting a two-week deadline for putting down the rebellion. "This state of affairs cannot be tolerated on Russian territory."

Russian jets attacked guerrilla positions, and officials said artillery and mortar assaults drove scores of combatants from two of at least four villages they had occupied over the weekend. But by evening, Russian officials acknowledged that the rebels had mortared an airfield in the Dagestani town of Botlikh, destroyed two helicopters and forced visiting army chief of staff Anatoly Kvashnin and several other generals to take cover.

Russian officials said two soldiers have died since counterattacks on the guerrillas began Sunday. A Dagestani official said five Russian policemen were killed by friendly fire, but Russia denied hitting its own forces.

Meanwhile, Georgia complained today that Russian jets dropped bombs on its territory, injuring two citizens. Russia said it would investigate that claim.

Viktor Kazantsev, the regional military commander, said he is calling up local reserve units, and Moscow police said they are on the watch for terrorism in the capital, more than 800 miles northwest of the area of conflict.

The surge in fighting--and incomplete and contradictory information in Moscow--harkens back to Russia's disastrous war in Chechnya. Moscow explains the current conflict with charges that Chechnya is trying to expand its self-proclaimed Islamic republic into Dagestan. The Russians say that mercenaries are fighting under the command of Shamil Basayev, a notorious Chechen commander.

The Chechen president, Aslan Maskhadov, denied the accusation and said Russian and Dagestani officials are to blame. He said Russia drove persecuted Dagestanis into Chechnya, and, angered, they have now returned home. Chechnya has nothing to do with this conflict, he insisted.

But a Dagestani group called Islamic Shura, or council, issued an independence declaration for their home province today in Grozny, the Chechen capital. According to copies faxed to news agencies, the Shura called on Chechens to help "the Muslims of Dagestan against infidels for the liberation of the Islamic state."

How much support the Shura might have in ethnically complex Dagestan is an open question. The mountainous region is a mix of dozens of ethnic groups, and it is far from clear if rebels could find support from one valley to the next. The region where recent fighting broke out is a hodgepodge of Chechen and other nationalities.

Some Western diplomats here say Russia overreacted to a minor conflict--although they acknowledge that it would be hard to ignore the persistent toll on its forces during a year of skirmishes. Several dozen police have been killed in armed attacks this year.

As soon as he was picked on Monday, Putin pledged to keep Russia stable, calling it a first priority. Today, he awoke to negative reviews of the shake-up that brought him to power. In political parlors and on the street, Russians regarded Yeltsin's ouster of prime minister Sergei Stepashin as capricious.

Yeltsin also anointed Putin his heir apparent in the election scheduled for next summer. Some observers found the announcement laughable, given that the public holds Yeltsin in very low esteem.

"By declaring Putin to be his successor, Yeltsin effectively nullified [Putin's] chances. As of now in the public mind, Putin is the Kremlin's man, and that will hardly endear him to society," said Boris Nemtsov, a former deputy prime minister and designated heir who saw his popularity collapse because of his association with Yeltsin and failed economic policies.

Random interviews showed that Russia's frequent changes in government leaders--four in the past 17 months--have sapped interest in politics. "Putin? Who's he? Why is he better than Stepashin, or for that matter [Yevgeny] Primakov?" queried jewelry salesman Vyacheslav Mironov, ticking off the names of Yeltsin's three last premiers. "We hardly get to know how to spell their names, and they're gone."

Zhenia Belov, a fruit vendor at Kiev Station market, also said he felt alienated from Kremlin politics.

"I don't put my eye on this political business," he said. "I keep my eye on kopecks [pennies] and just hope Granddad" -- Yeltsin -- "doesn't make a disaster."

At a nearby flower stall, one buyer exclaimed: "I thought Primakov was still prime minister. Who can keep up?"

CAPTION: A Russian sniper safeguards a helicopter landing in Dagestan, where Islamic militants are in revolt. The new prime minister vowed to reestablish order.