Slovenian President Borut Pahor expressed his concern on Monday after internet footage showed masked members of an armed group led by a fringe politician conducting training exercises.
Former presidential candidate Andrej Sisko told Reuters that his group would secure order if necessary, adding that it was doing nothing illegal - although he acknowledged that the weapons it uses have not been registered with the Slovenian authorities.
The president said there was no place for such a group in the European Union member state.
"President Pahor stresses that Slovenia is a safe country in which no unauthorized person needs or is allowed to ... illegally care for the security of the country and its borders," Pahor's cabinet said in a statement.
Photos on websites and in local media show up to 50 masked people with guns led by an unmasked Sisko, who won only 2.2 percent of the vote when he ran for president last year.
Sisko said the group called the "Guard of Stajerska," named after a region of northeastern Slovenia, consists of "several hundred people", adding that these were volunteers who "will secure public peace and order" if needed.
"The police have not visited me so far but I expect their visit. We are doing nothing wrong and we would be even interested in cooperating with the police," Sisko said.
The police said the force had started an investigation into the matter.
Sisko also attacked multiculturalism, saying the country should accept immigrants only if they accept Slovenian culture.
He also leads the center-right United Slovenia Movement, which got 0.6 percent of the vote in a June general election and failed to make it to parliament. The party has no connection to the military group, he said.
Anti-immigrant sentiment has increased in Slovenia since 2015 and 2016 when almost half a million migrants crossed the country on their way to richer EU states.
The number of requests for an asylum in Slovenia has risen significantly from 277 in the whole of 2015 to 1,717 so far this year. However, only 77 people have been granted an asylum in 2018 versus 152 in the whole of 2017, interior ministry data showed.
An anti-immigrant stand helped the center-right Slovenian Democratic Party to win most votes at the June election but the party lacked coalition partners to form a government.
As a consequence a minority government of five center-left parties is due to be confirmed in the parliament next week.