"A total of 66 pigs have died in the past 24 hours," a statement read.
Some 1,775 pigs have been culled in the republic following the outbreak, while over 7,000 potentially-infected animals have yet to be destroyed.
Outbreaks of the highly contagious virus are rare outside Africa, but last spring, Georgia, which borders on North Ossetia, saw outbreaks in 10 regions. A total of 20,000 pigs were culled.
Preliminary reports said that the infection may have been brought in by wild pigs. The virus can survive for up to 15 weeks in raw pork, and up to six months in processed meat.
The virus, which causes lethal hemorrhagic disease in pigs, does not pose a threat to humans.
The area has been cordoned off, and all the local pigs will be culled as a preventive measure. Around 174 people have been deployed to guard the province's border, to ensure that no pork products are taken out of North Ossetia.