Press TV say the journalists were arrested by a militia while driving late at night and taking photographs
French news agency AFP has reported that at a conference on Sunday commander Faraj Swehli told journalists that the two men - identified as reporter Nicholas Davies and cameraman Gareth Montgomery-Johnson - "were still being questioned because incriminating evidence had been found in their possession".
In an interview with Press TV, an English-language state-owned broadcaster based in Iran, Montgomery-Johnson's sister Mel Gribble said she did not believe the allegations.
"He's got accreditation and legitimately he's out there as a cameraman, journalist," she said. She added that their mother is "paralysed with anxiousness".
The BBC has reported that the "Libyan Prime Minister's office and the interior ministry told the BBC that they knew nothing of the allegations of spying".
Davies and Montgomery-Johnson were detained on 21 February with "several locals" in Tripoli, Press TV announced at the time.
On Saturday the broadcaster said "the whereabouts of Press TV’s journalists remain unknown".
"An official at the Saraya Swehli militia told Human Rights Watch that the militia had stopped the men because they were driving late at night in Tripoli and taking photographs, which the militia found suspicious. Militia members later accused the two journalists of not having the proper immigration papers.
"Although Libya's National Transitional Council has granted Human Rights Watch permission to access all detention facilities, the militia has blocked access to the team."
A spokesperson for the Foreign and Commonwealth Office said: "We are providing consular assistance to the two men. The embassy in Tripoli is doing everything that it can to assist the two individuals."