Acting Russian President Vladimir Putin spent his first night in power in war-ravaged Chechnya, visiting troops and declaring that a key task facing Russia's next elected leader will be solving the problems in the breakaway region.

Putin's trip to Chechnya came just hours after Boris Yeltsin's surprise resignation. He visited the pacified town of Gudermes to award 200 officers hunting knives inscribed before his unexpected elevation, and bearing only his title as prime minister.

"The trip was planned about a month ago," Putin told reporters in Dagestan, the Russian region east of Chechnya. "We did not know that Boris Nikolayevich [Yeltsin] would take the decision he did."

But Putin sounded themes that he is likely to press during his presidential campaign in the next three months. Speaking in a hangar-like building in Gudermes, he equated victory in Chechnya with the preservation of Russia. "This is not simply about restoring honor and dignity to the country. This is about how to bring about the end of the breakup of Russia," he told the soldiers. "That is your fundamental goal."

Putin has not publicly outlined his plans for the country since Yeltsin stepped down on New Year's Eve. He told reporters traveling with him that as acting president he would consider changes in the cabinet he inherited from Yeltsin, but focused his remarks on the war in Chechnya, the issue that has propelled him to popularity.

In Washington, President Clinton congratulated Putin on being selected and assured him that "we are always together on the core points," White House spokesman Joe Lockhart said. In a 10-minute morning telephone call, Clinton told Putin he believes the new leader is "off to a good start," and that the transition is "encouraging for democracy in Russia," the Associated Press reported.

The energy and determination Putin projects appeals to the Russian public. His New Year's performance contrasted with the activities of many of Russia's political and financial elite, who spent New Year's Eve at a gala dinner and concert at the Bolshoi Theater. Seats reserved for Putin and his wife were empty.

Television reports noted the bravery Putin showed by taking the trip. Putin's helicopter was denied permission to land in Gudermes, so he traveled by road, a dangerous act given the chance of a guerrilla ambush.

While Putin was in Gudermes, the Chechen capital of Grozny 20 miles away was under a fierce air assault. Russian troops have been trying to seize Grozny for a week, but Chechen defenders have used sniper fire, mortars and rocket-propelled grenades to keep them at the edge of the city.

Television footage from mountain overlooks shows devastated buildings and continuous shelling and bombing. On Friday, Russia fired three Scud ballistic missiles into Chechnya, U.S. officials reported. Such is the battering of Grozny that, when it is not foggy, the city is still encased in a smoky haze caused by fires and soot from explosions. Thousands of civilians reportedly are trapped in the city.

Fighting is also widespread south of Grozny, where the Russians are trying to dislodge rebels from mountain hamlets and block infiltration of ethnic Chechen rebels from Georgia.

Russian casualties have been steady, and reportedly relatively heavy the past few days. On New Year's Eve, eight Russian soldiers were killed, according to Gen. Vadim Timchenko, speaking from Mozdok, the campaign's military headquarters about 60 miles northwest of Grozny. Military officials told independent NTV television that as many as 10 soldiers a day had been killed. "Bandit groups are putting up fierce resistance in Grozny. We have to fight for every street, every house," said Gen. Valery Zhuravel.

In an interview Thursday with the Reuters news agency from a secret location near Grozny, Chechen President Aslan Maskhadov said that the war had barely begun. He said his forces were inflicting heavy losses on the Russians and repeated his call for internationally supervised peace talks.

One of the risks for Putin is that the war could go sour before presidential elections likely to be held in March. It may be difficult to sustain the notion that Russia is only fighting bandits and terrorists as it continues to suffer significant casualties. Official figures, which rise and fall, put the number at about 450 Russians killed in the four-month-old campaign.

In an apparent attempt to preempt criticism, Putin said, "Whoever will become the future president of Russia will be obligated to solve the problem of fighting terrorism. He will be obligated to solve the tasks . . . in Chechnya."

He repeated the bottom line for negotiations with the separatists: renunciation of terrorism; turning over fugitive Chechens; and the release of all kidnap victims.

Putin is popular among Russian generals, some of whom have threatened to resign if the assault on Chechnya is curtailed. In a rare foray into politics, Zhuravel told NTV that the military supports Putin's appointment. "We not only understand this, but approve of it and think it is good for Russia," he said.

Chechen officials expressed disappointment with Putin's initial remarks on the crisis as acting president. "Each day, the war is widening the gulf between Russia and Chechnya," Chechen Vice President Vakha Arsanov told the Interfax news agency.

Yeltsin was absent from public view today and reportedly resting at his country home near Moscow.

The lightning handover of power created a national sensation, but not so much as to upset Russia's celebration of New Year's. So many officials abandoned Moscow for home or the countryside around the capital that Putin canceled a meeting scheduled for Sunday with party leaders in the newly elected legislature.

CAPTION: Acting President Vladimir Putin signs autographs for Russian soldiers in Gudermes, east of the Chechen capital.