Army and police units on Wednesday searched for members of a 200to 300-man force that raided the city of Nazran and three villages early on Tuesday, inflicting heavy casualties and extensive damage at strategic facilities.
Five fighters were reported captured and helicopter missile strikes were mounted on forests where others were believed to be hiding.
Casualty reports varied greatly, but a spokesman for the republican government said 92 people, most of them security officials, were killed and 120 more were wounded in the fighting early on Tuesday.
Dozens of people were being treated in hospital for gunshot and grenade blast wounds after the fighters targeted numerous sites, including the republic's interior ministry, a police station and a border guard command post.
The Russian army were nowhere
in sight when attack happened
During the six-hour assault, the fighters reportedly shot down anyone they encountered who was believed to be an official.
Ingushetia's Interior Minister Abukar Kostoyev, his deputy and the Nazran district prosecutor were among the dead. A local United Nations worker was caught in crossfire and killed while driving through Nazran.
In conversations about the assault, opinion varied from admiration for its organisation - the fighters controlled the main highway through the republic for several hours before melting away as dawn broke - to dread that the action would be followed by mop-up operations as authorities sought out those behind the strikes.
"You've got to hand it to them - it was beautifully organised," a local resident Ali said. "They took them completely by surprise and retreated before they could do anything about it."
Meanwhile, there was mounting criticism of the unpreparedness of the security forces to repel the incursion launched from Chechnya and the republic of North Ossetia.
"You've got to hand
it to them - it was beautifully organised"
"There is a Caucasus war on," the Kommersant business daily gravely announced in a banner headline. "The fighters took control of Ingushetia for several hours."
"Why were federal and republican authorities once again taken by surprise? Do we have functioning military intelligence in this country?" wrote the Nezavisimaya Gazeta newspaper.
"What does the FSB domestic intelligence service do and what do our border guards protect?"
The span and impact of the attack refutes Kremlin claims that separatist Chechen fighters are all but beaten after almost five years of fighting with federal forces.