Russia has offered 300m roubles ($10m) for information leading to the arrest of Chechen rebel leaders Shamil Basayev and Aslan Maskhadov.
The two leaders have been wanted by Russia for years
Security services want any information that could help to "neutralise" the two following the Beslan school siege.
The regional government in North Ossetia is resigning, the republic's president, Alexander Dzasokhov, told angry protesters.
He said officials guilty of failings would be punished.
Repeatedly interrupted by calls of "Resign! Resign!" he said that he too was considering his position.
Tempers also continued to run high in Beslan itself, with more anti-government demonstrations, and more funerals for those killed in the siege.
"If he comes near me I will kill him," said Izeta Khugayeva, who lost her sister and niece in the siege, said of Mr Dzasokhov, as relatives held a vigil outside the school.
At least 326 people were killed, about half of them children, and 727 wounded, Prosecutor General Vladimir Ustinov said on Wednesday, revising the death toll down from 335. More than 100 bodies have yet to be identified.
Mr Ustinov said the bloody climax to the siege seemed to have begun when the hostage-takers were rearranging explosives in the school gymnasium and accidentally detonated one of them.
He said the hostage-takers had gathered in a forest before on 1 September then driven to the school with a lorry and two jeeps packed with weapons and explosives.
Twelve had now been identified, he added, but gave no details of names or nationalities.
The town's children were celebrating the start of the new school year with parents and staff a week ago when they were taken hostage. The crisis ended in massive bloodshed on Friday.
In response to the tragedy, European Parliament president Josep Borrell on Wednesday called on schools throughout the EU to observe a minute's silence on 14 September.
The Russian army's Chief of Staff, General Yuri Baluevsky, said Moscow planned to launch pre-emptive strikes on terrorist bases "in any region of the world".
A spokesman for Mr Maskhadov, Ahmed Zakayev, described the threat as a "disturbing signal for civilised countries" and said it set a dangerous precedent.
"It is a warning to other European countries that
Russia may come and carry out an assassination on your soil
at any moment," he said.
However, analysts said the doctrine might only be applied to former Soviet countries - such as Georgia, to the south of Chechnya, which Russia has accused of providing a haven for Chechen fighters.
The two rebel leaders attracting offers of rewards from the Federal Security Bureau have been wanted by Russian authorities for years in connection with various attacks.
Mr Maskhadov was elected president of Chechnya in 1997, but Moscow now considers him a terrorist.
Mr Basayev is a Chechen field commander, accused of masterminding operations and known for his extreme brutality.
He led the first Chechen mass hostage-taking in the southern Russian town of Budyonnovsk in 1995 and he claimed to have organised the seizing of a Moscow theatre in 2002, during which some 130 people died.