The Interior Ministry said the gunmen were suspected of shooting at the republic's most senior Muslim cleric and his son earlier this week.
Isa Khamkhoyev, the mufti of Ingushetia was slightly wounded, his son was reportedly seriously hurt in the attack.
The siege in Malgobek is the latest in a series of similar incidents in areas surrounding Chechnya.
In Chechnya, meanwhile, four suspected militants were killed in a clash with security forces.
(Interfax, AP, Reuters)
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