In three hours of phone negotiations, officials on Thursday said they offered the hostage-takers safe passage out of the region and also to exchange the trapped children - some as young as five - with adults. Both offers were turned down.
There was conflicting information about the hostage-takers' demands, with some initial reports saying they have sought the withdrawal of Russian troops from Chechnya.
Camouflaged troops surrounded the school in the North Ossetian town of Beslan on Wednesday while distraught parents crowded outside police cordons demanding information and accusing the government of failing to protect their children.
Wrapped in suicide-bomb belts, the hostage-takers are threatening to blow up the building and kill the captives if the school was stormed by Russian troops.
Eight people died of their wounds on Wednesday, according to Salam al-Ubaiby, Aljazeera correspondent reporting from Beslan.
The kidnappers have only allowed the school's doctor to enter and negotiate with them about delivering supplies like food and water to the hostages.
The captors belong to the Shuhada (Martyrs) Riyadh al-Salhin group, one of whose cells was responsible for the Moscow theatre siege in October 2002.
"I have been here all day, waiting for anything," said Svetlana Tskayeva, a woman whose grown-up daughter and three grandchildren are among the hostages.
"I am not hearing anything, they are not telling us anything," she said. "It's awful, it's frightening."
The Beslan school siege began less than 24 hours after a human bomber self-detonated outside a Moscow railway station on Tuesday, killing at least nine people.
Apart from pupils, the hostages
include teachers and parents
On Wednesday, the attackers - men and women - drove up in a covered truck and stormed the building where children were preparing for the first day of the school year.
Most of the hostages were herded into the school gym, but others, primarily children, were ordered to stand at the windows, police spokesman Alexei Polyansky said.
The school covers grades 1-11, but officials said that most of the children taken hostage were under 14 years of age.
Gunfire broke out after the raid and regional emergency officials said 11 men and two women suffered gunshot wounds.
One girl lay wounded on the grounds near the school, but emergency workers could not reach her because the area was coming under fire.
Russian media reported that as many as 50 children managed to flee the school in the chaos of the raid.
Kazbek Dzantiyev, head of the region's Interior Ministry, said group has threatened that "for every destroyed fighter, they will kill 50 children and for every injured fighter 20 children".
While officials have not linked the Beslan group to Chechen fighters, the event brought back nightmarish memories of the hostage-taking at a Moscow theatre by Chechen separatists in 2002, during which 130 spectators died after police used a poison gas when they stormed the building.
Faced with the latest crisis, Russian President Vladimir Putin has broken off his seaside holiday to return to Moscow.
"I am not hearing anything, they are not telling us anything. It's awful, it's frightening"
Mother of one of the hostages
On Tuesday, at the Black Sea resort of Sochi, the Russian leader had met German Chancellor Gerhard Schroeder and French President Jacques Chirac.
Putin had been due to visit Turkey this week but has cancelled his plans.
The Kremlin said Putin summoned his interior minister and the head of the FSB security service to discuss the crisis.