-- The guerrillas who took over a school in southern Russia last week argued heatedly with each other over whether to abandon the siege in the moments leading up to the firestorm of explosions and shooting that killed hundreds of children and adults, Russian officials said Monday.

Russian special services had a surveillance tape of the militants fighting about whether to stay or flee just before a bomb they had planted in the school gym went off, prompting Russian commandos to storm the building, a senior Kremlin official said. Investigators were exploring whether the bomb detonated by accident or as a result of the internal dispute.

As more details surfaced about the massacre at School No. 1 in the town of Beslan, a partial picture emerged of the guerrillas and the four men who led them into the school, where investigators say they took orders by phone from a Chechen commander, Shamil Basayev.

The leaders, they said, included a bodyguard of Basayev's and a former police officer who turned against authorities and led a bloody attack in the neighboring republic of Ingushetia last June.

All four leaders were killed in the battle at the school, authorities say.

The Kremlin official, Aslanbek Aslakhanov, said in an interview that more than 20 elite Russian commandos were killed in the day-long battle that began Friday, many of them accidentally shot in the back by civilian vigilantes who rushed to the school to fight for their children. The previously undisclosed death toll, he said, surpasses any in the history of the famed Alpha and Vympel special forces units.

In sorting through the origins of the hostage crisis, Russian officials said they had concluded that the strike against a target outside Chechnya, the scene of nearly 10 years of intermittent fighting, was part of a broader strategy to reignite the entire North Caucasus, a historically volatile region of mixed ethnic and religious groups. While the government has admitted to lying about the scope of the hostage crisis at first, its analysis about the goals and Chechen sponsorship coincides with that of independent specialists.

"The puppet leaders who organized these fierce incursions, they are attempting to destabilize the situation in the North Caucasus and make one people go against another," said Aslakhanov, President Vladimir Putin's top Chechnya adviser. "They are inciting old grudges and unsolved problems."

To bolster their version of events, Russian officials put a Chechen man they identified as a captured guerrilla on state television Monday night to make the first public statement by any of those involved in seizing the school. Visibly injured and having trouble talking, the prisoner described one of the ring leaders giving the orders for the attack.

"We gathered in the forest and the Colonel -- it's his nickname -- and they said we must seize the school in Beslan," said the man, who had short, dark hair and no beard. He said the orders came from Basayev and another Chechen commander, Aslan Maskhadov, and that his group included Arabs and Uzbeks as well as Chechens and people of other nationalities. "When we asked the Colonel why we must do it, he said, 'Because we need to start war in the entire territory of the North Caucasus.' "

Many of the guerrillas who seized the Beslan school in the Russian republic of North Ossetia took part in raids in Ingushetia in June that killed 90 people, investigators said Monday. "They're the same people that attacked Ingushetia," said Musa Apiyev, deputy interior minister in Ingushetia. "They're traveling, they're moving from place to place, exploiting the weak spots in our positions, and they're running from spot to spot committing their dark crimes."

Ingushetia and North Ossetia, located south and west of Chechnya, are dominated by different ethnic groups and fought a brief territorial war in 1992. Relations have remained tense since. In the days after the hostage crisis at the school, many Ossetians have blamed the Ingush and warned of retribution.

"It appears to be a deliberate provocation to reignite the conflict between Ingushetia and North Ossetia, to extend the range of the chaos," said Fiona Hill, a scholar at the Brookings Institution in Washington. "It's very easy to stir up the region if you want to, and somebody wants to. This is a wake-up call. The whole of the Caucasus is going to go up at this rate."

Putin raised the specter of the region breaking apart from Moscow during a meeting with Hill and other visiting Westerners late Monday. "There's a Yugoslavia variant here," he said, according to notes taken by Eileen O'Connor, a participant. "It would be difficult to imagine the consequences for the rest of the world. Bear in mind Russia is a nuclear power."

The four leaders inside the school represented the spectrum of the region's ethnic groups: a Chechen, a Russian, an Ingush and an Ossetian, according to tentative identifications by Russian officials. What remained unclear was the extent of the involvement of Arab fighters, if any. Russian officials initially said 10 of the hostage takers were Arabs, but surviving hostages said in interviews that they saw no Arabs and not one was identified as a leader to outside negotiators.

Russian investigators are checking out reports from an unidentified Western intelligence service suggesting that some of the attackers came from Jordan and Syria, according to a source briefed on the government's investigation who spoke on condition of anonymity because of the sensitivity of the matter. An Islamic group tied to al Qaeda's second-in-command, Ayman Zawahiri, has claimed responsibility for the attack.

But some analysts remained skeptical, arguing that the Russians were exaggerating the Arab connection so Putin could claim to be fighting international terrorists rather than domestic nationalists.

"It could be there were advisers from the Middle East, but initiating the plan, executing it, belonged to locals," said Alexei Malashenko, a regional specialist at the Carnegie Moscow Center, a research organization.

Calling the shots, according to Russian investigators, was Basayev, the brutal guerrilla leader who has fought the Russians in two wars over the past 10 years and been designated a terrorist by the United States and United Nations.

Basayev stormed a Russian hospital in 1995 and took more than 1,000 patients and doctors hostage and sponsored the capture of a Moscow theater in 2002 that led to the deaths of 129 civilians.

In apparent retaliation for the attack on the school, Russian authorities rounded up relatives of Basayev and Maskhadov in Chechnya on the second day of the siege. "I think it was to be hostages for hostages," Akhmed Zakayev, a Maskhadov lieutenant, said in an interview. Twenty of Maskhadov's relatives were detained and later released, Zakayev said.

Col. Ilya Shabalkin, a military spokesman, said the family members were held at the main base in Chechnya for their own protection. "We hid them in Khankala for two days to avoid vengeance actions against them," he said.

The 32 guerrillas who seized School No. 1 in Beslan managed to evade detection on the way to the school by traveling along forest roads and picking up at least one and perhaps several police officers along the way who helped get them through checkpoints, investigators said. "Most likely these people were made to do that under threat," said Apiyev, Ingushetia's deputy interior minister.

Investigators are still trying to piece together how the first bomb, which triggered the confrontation, went off. Aslakhanov said one theory was that a guerrilla was confused over the wires and connected the wrong ones. But Aslakhanov also pointed to the internal rift.

"The special services have a recording of a split among the terrorists," he said. "Some wanted to leave and others wanted to stay. The conflict was happening and at that moment this tragic explosion occurred."

The four commanders of the school operation were identified by the code names Abdullah, Fantomas, the Colonel and Magas.

Abdullah, described as an Ossetian named Vladimir Khodoyev, fought alongside Basayev in the past. Fantomas was a Basayev bodyguard who may be Chechen or Russian, officials said. The Colonel appeared to be a Russian who many of the hostages remembered as a regular presence in the gym.

The fourth commander drew the most attention, a man known as Magas, a nickname taken from Ingushetia's capital. Magas emerged this year as head of the Ingush Jamaat, a militant group allied with the Chechen guerrillas, and he led the June raids in his native Ingushetia, killing dozens of police officers and prosecutors. He has defied efforts to hunt him down. Russian authorities twice reported killing him this summer, only to discover they were wrong.

"I know that he's dangerous," said Nurdi Doklayev, a Nazran city investigator who examined the June raids. "All the adjectives -- cruel, bad, angry -- could fit this guy because he's killing people."

Authorities said they first heard the name Magas after an assassination attempt in April against Ingushetia's president, Murat Zyazikov, and began trying to determine who he was. "Until recently, Magas was a big mystery to us," Apiyev said.

At first, authorities thought his real name was Magomed Yevloyev. A man by that name was killed in the town of Malgobek, and the military spokesman, Shabalkin, declared then that he had "no doubt" Magas was dead. But it turned out the dead man was an unrelated murder suspect with the same name.

Then another suspect named Magomed Yevloyev was killed, this time in Galashki, but he, too, proved not to be Magas.

Authorities said Monday that they have now identified Magas as Ali Taziyev, 30, an Ingush police officer who disappeared in 1998. "He is Magas," said Dzhabrail Kostoyev, the region's first deputy interior minister. "For a long time we had him recorded as a loss. And all of a sudden he came to the surface in recent events."

Police raided Taziyev's family home in Nazran on Sunday, bringing in metal detectors and trained dogs to search for weapons for five hours. In an interview at the house Monday, his relatives rejected the idea that Taziyev was Magas and said they believed he was killed years ago. "If he was alive, he would have sent us a letter, something," his brother Aslan said.

The seventh of 10 children, Taziyev disappeared on Oct. 10, 1998, while he was working as a guard for a local official. He and another police officer were escorting the official's wife around a market when the three were kidnapped by Chechens, according to relatives and police. The wife was ransomed late in 1999, the other officer's body was found in 2000 and the still-missing Taziyev was officially declared dead in 2001.

Officials at his old ministry now say they believe he may have already been working with the Chechens at the time of the kidnapping and helped stage it or went over to their side after being taken prisoner. "Either he was interested in money or was under threat of death regularly and later probably he was zombied," Apiyev said.

Taziyev would not be the only police officer to switch sides. Several of the 30 people arrested after the June raids here were members of the local militia, including a captain from internal affairs who allegedly helped the guerrillas get into the region to begin their attack.

Officials said militants increasingly have been recruiting in Ingushetia. "They all gather underground," Girikhan Khazbiyev, a local prosecutor, said. "They live among us. They're here. At the necessary moment, they get together and act."

Glasser reported from Moscow.

In Beslan, family and friends buried the victims of the school siege as rain poured down on mourners and gravediggers. Funeral processions arrived one after another, with as many as five people buried at the same time. Story, Page A14 In St. Petersburg, a woman holds a poster reading "Only cowards fight with kids," during a rally to condemn the attackers of the school in Beslan. At left, the alleged guerrilla Magas. At right, a man described as a part of the group that seized the school.