Russian forces are pursuing rebels who carried out bloody overnight attacks in the southern region of Ingushetia.
The rebels burned down a police station in Nazran
At least 57 people including the acting interior minister and his deputy were killed during the assaults blamed on fighters from neighbouring Chechnya.
The authorities said the rebels left their vehicles in the border town of Galashki before fleeing into Chechnya.
Russian President Vladimir Putin - who flew to the area attacked - said the guerrillas must be "destroyed".
Mainly Muslim population, ethnically close to the Chechens
Suffers occasional overspill of war in Chechnya
Last major battle between fighters and Russian forces in October 2002
"Those whom it is possible to take alive must be handed over to the courts," Mr Putin told leading security officials in a televised meeting.
But during a lightning visit to Ingushetia, he added that "judging by what is going on here, the federal centre is not doing enough to defend the republic".
Mr Putin pledged to act swiftly to step up security in the restive region, especially around the airport of the main Ingush town of Nazran.
The president's helicopter visit to Ingushetia was intended to show that he was still in control despite the audacious and carefully orchestrated attacks, the BBC's Sarah Rainsford in Moscow reports.
Thousands of troops, including reinforcements sent across the border from Chechnya, are involved in the hunt for the rebels. They are being supported by helicopter gunships.
Three days of mourning have been declared in Ingushetia
The series of attacks by some 200 fighters was the biggest armed operation by rebels in Ingushetia since fighting broke out between separatists and the Russian authorities in neighbouring Chechnya more than a decade ago.
The rebels seized the interior ministry building in Nazran and held it for several hours before leaving it a burnt-out wreck. Acting regional Interior Minister Abukar Kostoyev, his deputy and another senior official were killed there.
The rebels also attacked border guard posts in Nazran, Karabulak and Sleptsovskaya.
At least 57 people - including members of the Ingush interior ministry, the federal security service, border guard and
prosecution service - died in the raids, the Russian authorities said.
At least two rebels are also reported to have died.
The regional authorities have declared three days of mourning.
Ingush President Murat Zyazikov told Interfax news agency that a large number of weapons and ammunition were missing from police depots.
Last week the Chechen rebel leader, Aslan Maskhadov, warned of impending large-scale attacks.
Moscow is preparing for an August election to replace Kremlin-backed Chechen President Akhmad Kadyrov, who was killed last month in a bomb attack that was seen as a significant blow to President Putin's efforts to bring stability to Chechnya.
BBC Moscow correspondent Stephen Dalziel says the latest attacks show the rebels are still a force to be reckoned with.