Terrorists holding hundreds of hostages at a school in south Russia freed as many as 31 women and children Thursday afternoon, some of them babies, Russian officials said, as the number of people believe trapped in the building more than doubled by some counts.

Local official Lev Dzugayev said 26 women and children of various ages were released and called their freedom "the first success," expressing hope for further progress in negotiations. Other officials also said 26 were freed, but an official at the headquarters for the rescue operation said another group of five people was released separately.

Dzugayev also said his earlier statement that 354 hostage were seized might have been too low, and many in the anxious crowds in Beslan said they believed the number was much higher. "Putin: at least 800 people are being held hostage," read a sign held up for television cameras.

Between 15 and 24 militants were thought to be in the school, which had students from grades one to 11. Also taken hostage in the standoff were some parents who were bringing their older children to school while carrying with them babies or preschoolers.

A crowd of hostages' relatives keeping vigil outside the school was shaken when a pair of explosions went off just ahead of the release. Officials said the terrorists fired rocket-propelled grenades at two cars that got too close to the school.

The developments came after a night of telephone negotiations between Russian authorities and the terrorists, who stormed the school Wednesday, rounding up hundreds of children and adults into a gym and threatening to blow up the building if police launch an assault.

Security agents in soldiers' fatigues could be seen carrying infants and escorting women and small children out of the school, where militants held hundreds hostage for a second day.

The freed hostages were put into cars and taken away — including one woman with a naked child and a baby — but the standoff continued.

The release was the result of negotiations with the terrorists, officials told FOX. Authorities were exercising caution as the extremists were said to be heavily armed — some with bombs strapped to their bodies.

Officials expressed hope that negotiations would bring more progress in the standoff in southern Russia.

The school in Beslan, a town of about 30,000, is in North Ossetia (search), near the war-torn republic of Chechnya (search) where separatist rebels have been fighting Russian forces since 1999.

Suspicion in the raid fell on Chechen militants, although no claim of responsibility has been made.

A crowd of waiting relatives and friends immediately swarmed around Dzugayev, an aide to the North Ossetian president, in an attempt to find out information about who was freed after Dzugayev first announced the release.

Casualty reports in the raid varied widely, but an official in the joint-command operation for the crisis said on condition of anonymity early Thursday that 16 people were killed — 12 inside the school, two who died in hospital and two others whose bodies still lay outside the school and could not be removed because of gunfire. Thirteen others were wounded.

However, Dzugayev said that seven were killed.

The hostages were set free shortly after two large blasts went off near the school. Terrorists stormed the school early Wednesday, making a number of demands involving Chechnya.

Parents of the schoolchildren had begged police not to storm the building out of fear that a forced entry would enrage the terrorists into killing the hostages, FOX News has learned.

The militants who stormed the school Wednesday had threatened to blow it up if Russian forces launched an assault to free the hostages — but there was no sign that any operation or battle was under way.

Russian authorities and the militants spent Wednesday night negotiating on the telephone.

Valery Andreyev, the Federal Security Service's chief in North Ossetia, seemed to rule out the immediate use of force against the hostage-takers.

"There is no alternative to dialogue," the ITAR-Tass news agency quoted him as saying. "One should expect long and tense negotiations."

Sporadic gunfire chattered in the area through the night, keeping the crowds of relatives around the school on edge. On Thursday — 30 hours into the crisis — two large explosions about 10 minutes apart rocked the area, raising a cloud of black smoke.

Officials at the crisis headquarters said the releases came after mediation by Ruslan Aushev, an Afghan war veteran and former president of the neighboring Ingushetia region who is a respected figure in Russia's troubled North Caucasus region.

In his first public comment on the raid, President Vladimir Putin (search) Thursday pledged to do everything possible to save the lives of the hundreds of hostages.

"We understand these acts are not only against private citizens of Russia but against Russia as a whole," Putin said in comments broadcast on Russian television during a Kremlin meeting with Jordan's King Abdullah II. "What is happening in North Ossetia is horrible.

"It's horrible not only because some of the hostages are children, but because this action can explode even a fragile balance of interconfessional and international relations in the region," Putin said.

Dzugayev said brief contact with the captors indicated they were treating the children "more or less acceptably" and were holding them separately from the adults.

He added that the attackers might be from Chechnya or another neighboring region, Ingushetia; relations between Ingush and Ossetians have been tense since an armed conflict in 1992.

But in Washington, a U.S. official speaking on condition of anonymity said the hostage-takers were believed to be Chechen rebels.

The hostage-taking came less than 24 hours after a bombing outside a Moscow subway station that killed at least nine people, and just over a week after near-simultaneous explosions blamed on terrorism caused two Russian planes to crash, killing all 90 people on board.

The recent bloodshed is a blow to Putin, who pledged five years ago to crush Chechnya's rebels but instead has seen the insurgents increasingly strike civilian targets beyond the republic's borders.

Heavily armed terrorists wearing masks descended on Middle School No. 1 shortly after 9 a.m. on the opening day of the new school year Wednesday. About a dozen people managed to escape by hiding in a boiler room, but hundreds of others were herded into the school gymnasium and some were placed at windows as human shields.

The terrorists sent out a list of demands and threatened that if police intervened, they would kill 50 children for every hostage-taker killed and 20 children for every hostage-taker injured, Kazbek Dzantiyev, head of the North Ossetia region's Interior Ministry, was quoted as telling ITAR-Tass.

Security forces surrounded the building, and militants perched a sniper on an upper floor. Since the seizure, militants have refused offers to deliver food and water to the school and are demanding the release of fighters detained over a series of attacks on police facilities in the nearby republic of Ingushetia.

The attackers demanded — and received — talks with a prominent pediatrician, Leonid Roshal (search), who aided hostages during the deadly seizure of a Moscow theater in 2002.

After contacts with the militants, Roshal said late Thursday that the captors had repeated their rejection of food, water and medicine for the hostages. He warned that an unsuccessful outcome of the hostage crisis "would mean war" in the region, and appealed to Chechens, Ingush and Ossetians to avoid bloodshed.

Law enforcement sources in North Ossetia and Inguhetia, speaking on condition of anomymity, said the hostage takers were believed to include Chechens, Ingush, Russians and at least one North Ossetian.

Elders from Chechnya and Ingushetia offered to act as stand-in hostages so that women and children could be released, Andreyev told NTV. He also said that some of the militants had been identified, and investigators were attempting to find their relatives and bring them to the school to help in the negotiations. Two Arab television stations had also offered to negotiate, he said.

The drama at the school came with memories still sharp from the deadly end to last major hostage-taking blamed on Chechens. In 2002, Chechen militants seized a Moscow theater, holding hundreds inside. That standoff ended when police pumped an unidentified knockout gas into the building — but the gas was responsible for almost all of the 129 hostage deaths.

Gennady Gudkov, a retired Federal Security Service colonel, said there is little chance that authorities will resort to a knockout gas this time — particularly since medical experts said it tended to have a stronger effect on children.

FOX News' Dana Lewis, Catherine Donaldson-Evans and The Associated Press contributed to this report.