Russia outlined conditions today for ending its punishing air attacks on Chechnya, demanding that Chechen leaders denounce terrorism and extradite "criminals" accused by Moscow of masterminding a recent series of apartment house bombings in which nearly 300 people have been killed.

Prime Minister Vladimir Putin set out the conditions, sketching for the first time Russia's goals in the chaotic southwestern region. Chechnya won de facto independence from Moscow three years ago after a brutal separatist war. A new conflict was ignited last month when a Chechen-led rebel force invaded the neighboring Russian region of Dagestan pledging to set up an Islamic state.

Putin's comments suggested a need to satisfy growing concern over where this conflict is heading. The week-long bombing campaign has prompted some Russians to worry that a ground war is next, with casualties, disruption to planned parliamentary and presidential elections and economic damage as results. Although a new survey showed that almost half the Russian populace approves of the aerial assault, 36 percent disapprove--despite wide public outrage at the apartment house bombings.

Putin told reporters that Russia has limited objectives in Chechnya. "We are expecting the Chechen leadership to finally condemn terrorism in explicit and definite terms," he said. He demanded they also "extradite the criminals" responsible for the apartment bombings and the invasion of Dagestan. Russia has not published a list of suspects, who are said to number 17, but officials have named Chechen militia leader Shamil Basayev and a shadowy, Saudi-born guerrilla named Khattab as the prime movers.

Putin's spokesman also said the Chechens must agree to help stop cross-border violence and regional crime.

Putin made his comments in conjunction with Russia's first diplomatic move to end the crisis, sending Magomedali Magomedov, who heads the Dagestani parliament, to meet Chechen President Aslan Maskhadov. Talks were supposed to take place inside Dagestan, but the trip ended in disarray. Dagestanis angry over the war blocked the convoy of each official. No new meeting date has been set.

It is uncertain how much authority Maskhadov exercises over Basayev, or for that matter, the country. Chechnya is divided by factional rivalries, and clan leaders control their own armies. Still, the invitation to Maskhadov suggested that Russia was hoping to secure his denunciation of the Chechens' cross-border incursions and thereby split Chechen ranks.

Concern that the conflict might expand into a ground war has been mounting in Moscow. Russians fear a repeat of the humiliation they suffered in the 1994-1996 war, which resulted in the deaths of thousands of Russian soldiers, the slaughter of many more Chechen rebels and civilians and de facto independence for Chechnya.

Russian generals boast they will tame the breakaway region and in effect reverse those results. Putin said this week that Russia will rely on air power to "eliminate the bandit formations," but he also speaks vaguely of "special operations" on land.

Today, the Segodnya newspaper published an elaborate account of a plan to conquer half of Chechnya and set up a puppet government. The invasion would be launched from positions now being established by Russia on Chechnya's borders.

In the meantime, Russian jets continue to pound Chechen targets near the capital, Grozny, and also in the far west and east. At least 70,000 refugees have flooded into Ingushetia, Chechnya's western neighbor in the Caucasus region, and many are camped out in makeshift shelters near the border.

If the the war is to expand, Russian leaders will have to consider public opinion, which was instrumental in prompting Russia's 1996 retreat from Chechnya.

Perhaps nowhere in Russia does the cry for revenge blend more uneasily with concern over the war than on Kashirskoye Highway in Moscow. About 120 Russians died there on Sept. 13 when an eight-story apartment building was demolished by an explosion. The site has been cleared of rubble, and only a tall wooden memorial cross and floral tributes mark the location now.

Even here, doubts about the war against Chechnya surface. Few believe that an air campaign will end the terrorism, and some think it is wrong to punish Chechens massively for the actions of a few. Most of all, no one seems to know what will happen next.

"I think bombing can be effective to a point, but then what? Eliminating the bandits from the air is not possible, and I'm opposed to a ground invasion," said Aleksander Vakhrameyev, a truck driver. "In an invasion, our people die."

Sergei Sarychev, who passed by the blast site to mourn his son-in-law, was skeptical of the bombing of Chechnya. "It is not likely to help. It gets at the whole population indiscriminately. But won't that only create more hate?" he asked, with tears in his eyes.

Zinaida Ivanova asked, "Who knows what to believe? How do we know Chechens did this? And if they did, will not the bombing mean more violence?"

"Terrorists are everywhere, and how many get punished?" asked Paulina Semyonvona. "Anyway, I'm not sure the bombing in Chechnya has to do with this. It seems to me the politicians wanted to bomb anyway. If they want to invade Chechnya, they'll find some other excuse."

More specific fears are registered at the offices of the Soldiers' Mothers Committee, a peace organization. Increasing numbers of parents have been inquiring about how to help their sons avoid the draft. The second phase of the twice-a-year call-up begins Friday.

The Mothers Committee was created during the first Chechen war in angry response to the lack of information, hundreds of missing soldiers, the inept battlefield command and ill-treatment of young Russian conscripts.

"People are afraid of a new Chechen war," said committee coordinator Valentina Melnikova. "Draftees are being sent to the front, and the parents believe they have not been trained properly. They think they are being sent to die."

Melnikova said such concerns have not yet built into protests, partly because the wounds from the terrorist bombings make Russians leery of expressing misgivings. Also, the outcome of the air war is not yet clear. "People have no information, so they are just waiting," she said. "It is a trap, I think. By the time we know, it will be too late."

CAPTION: Angry crowds blocked the roads leading to the Dagestani capital to prevent Chechen and Dagestani leaders from meeting.