"A gun battle is currently under way with remaining members of this armed group," a spokesman for the Ingushetia branch of the FSB was quoted by Interfax news agency as saying.
Speaking to Al Jazeera, Vyacheslav Matuzov, a former Russian diplomat, said: "The main source of all these clashes and disturbances [has] a social basis.
"After the dissolution of the Soviet Union, [the North Caucasus] republics were deprived of jobs, deprived of social security, deprived of social standards of life ... and this is the main cause increasing population.
"I don't think al-Qaeda or any outside sources play a main role in these disturbances.
"I don't exclude that some third party, especially based in Georgia, is using all this situation to encourage anti-Russian revolt in the southern regions, especially the North Caucasus."
Violence in the North Caucasus region has escalated in recent months, with clashes occurring regularly between security forces and separatist fighters.
Russia is attempting to crush an armed separatist movement in its mostly Muslim southern regions of Dagestan, Ingushetia and Chechnya, where federal forces fought two bloody wars against separatist groups in the 1990s.
The separatist movement has been largely led by Dokka Umarov, 45, the self-proclaimed leader of the "Caucasus Emirate", which has sought to unite various Muslim groups in the North Caucasus and establish Sharia rule in the region.
Local leaders in Ingushetia, with a population of around 300,000, say poverty and unemployment are fuelling the unrest.
Human-rights groups have criticised heavy-handed tactics by the security forces, saying they have created a groundswell of popular opposition to Moscow-backed officials.
But Russian officials blame the violence on groups of armed men, many driven by Islamist ideology, who they say have tried to overthrow Moscow's rule since 2002.