The near-simultaneous attacks late on Monday night against police headquarters, border guard stations and the Interior Ministry building in three towns and cities including Ingushetia's largest, Nazran, were believed to have been carried out by Chechen separatists.
The acting Ingush interior minister, Beslan Khamkhoyev, said that 15 buildings and police checkpoints were attacked in the overnight raids.
The fighters took 20 people captive and seized two trucks loaded with weapons and military equipment, said Aljazeera's correspondent in Moscow.
Thousands of Russian troops poured into the province, which enjoys the status of a republic within the Russian Federation, in pursuit of up to 200 fighters who had retreated into the dense forests on the border with Chechnya.
Ingush Interior Ministry spokesperson Yakhya Khadziyev earlier said at least 60 people had been injured and two of the attackers killed.
Clashes broke out between the suspected separatists and law-enforcement authorities after the coordinated attacks in the republic, which until recently housed tens of thousands of refugees who fled the fighting in Chechnya.
Many Russian soldiers are
reported to have been killed
A skirmish was also reported in the capital of Dagestan, a republic that lies east of Chechnya, but it appeared to be unrelated to the Ingushetia attacks.
Russia's President Vladimir Putin ordered authorities "to find and destroy" the raiders.
"Those who can be caught must be taken alive and brought to trial," Putin told a Kremlin meeting of police and security officials, in remarks aired on state television.
Later in a visit which took in a meeting with local officials in the Ingush capital, Magas, Putin said: "This is another attempt to frighten the Ingush, to frighten the republic's leadership, and to destabilise the situation."
Fighting raged around at least five police buildings and
checkpoints, according to the Ingushetiya.ru news website.
The Interior Ministry building in Nazran was reportedly ablaze, and residents in Karabulak heard automatic gunfire and overflying helicopters throughout the night.
Witnesses also reported seeing a military vehicle column come under gunfire a few minutes after entering Ingushetia from the neighbouring republic of North Ossetia.
Apart from the ministry building, the fighters attacked a major border guard building, setting it as well as Interior Ministry arms depots ablaze, the agencies said.
Acting Ingush Interior Minister Abukar Kostoyev was killed in the fighting. Ingush emergency services officials also said the health minister and a deputy interior minister had died.
The burnt-out hulk of an APC is
inspected by locals
Taking cover in their cellars, residents said they could hear the sound of grenade-launchers and small arms being used in what seemed like a major battle.
Police at the Chermen checkpoint on the North Ossetian border said that a 10-vehicle Russian military convoy had been ambushed en route to Nazran, about three kilometres away. Three vehicles were later seen returning to Vladikavkaz, the North Ossetian capital, carrying an unclear number of casualties.
Major General Ilya Shabalkin, spokesman for the Russian forces in Chechnya, said he believed the attacks were carried out by fighters recruited from both Ingushetia and Chechnya.
Chechnya's Interior Minister Alu Alkhanov, the Kremlin-supported candidate in Chechnya's Moscow-sponsored presidential election, said that he believed Chechen separatist leader Shamil Basayev, who has been behind some of the most audacious raids, was behind the assault.
Ingushetia, a mainly Muslim province, has witnessed numerous attacks in the past few years.
Ingushetia's pro-Moscow president, Murat Zyazikov, survived an assassination attempt on 6 April when an explosive-laden car rammed into his motorcade.
On 15 September 2003, the regional headquarters of Russia's security service, the FSB, was destroyed by a bomb attack ahead of Kremlin-organised presidential elections in the war-torn republic.
In May 2004 Chechen separatists succeeded in blowing up a stadium stand seating Akhmad Kadyrov killing the pro-Russian Chechen president.
Thousands of Chechen refugees, who had escaped the conflict to neighbouring Ingushetia, were forced to return to their homes when Russian authorities closed the last refugee camp in Satsita on the Chechen border.