Fringe politician Andrej Sisko said his group - seen conducting training drills - would "secure public peace and order" if needed.
President Pahor said there was no place for such a group in the "safe" country.
Police are investigating the group, which posed with assault rifles but denies being a paramilitary unit.
Videos posted on Facebook show some 70 masked people allegedly taking a "solemn oath".
The group is led by an unmasked Mr Sisko, who once served prison time for attempted murder.
He won 2.2% of the vote last year when he ran for president of the small EU state, which was once part of the former Yugoslavia.
He lost out to Mr Pahor, whose cabinet said in a statement: "President Pahor stresses that Slovenia is a safe country in which no unauthorised person needs or is allowed to...
illegally care for the security of the country and its borders."
Mr Sisko denied the group - called the Stajerska Guard after a north-eastern region - was doing anything illegal, telling Reuters news agency it was a voluntary defence force consisting of "several hundred people".
However, he conceded the weapons they carried had not been registered with authorities.
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