The attack occurred in the west of the republic at 2:00 a.m. local time (22:00 GMT) in the village of Chemulga, in Ingushetia's Sunzha district. According to preliminary information, five armed men shot dead a man and his son who had both formerly served in the police, the spokesman said.
Ingushetia has seen a rise in violence in the last year. The Russia-based human rights group, the Moscow Helsinki Group, said in September that the republic was on the verge of civil war as fighting between militants and authorities intensified. It also accused federal authorities of torture and abductions.
In a separate incident, a Russian motorized infantry officer was killed by unknown assailants late on Sunday evening in Buynaksk, in Russia's neighboring North Caucasus republic of Daghestan.
