Nicholas Davies and Gareth Montgomery-Johnson: 'We came here to report the news'
Welsh MP Jonathan Edwards said he was hopeful that the move meant the reporters would be allowed to return home "very soon".
Reporter Nicholas Davies and cameraman Gareth Montgomery-Johnson, who work for Iranian broadcaster Press TV, have been held since 22 February.
Militia leader Faraj al-Swehli told the Associated Press that the journalists were found with classified documents and pictures, including a database of mercenaries apparently hired by then-ruler Muammar Gaddafi. The pair have been handed over to the Libyan government's intelligence unit for further interrogation.
In a video clip recorded by the militia earlier this week, the journalists said they were in good condition. Montgomery-Johnson said in the video: "We are sorry for causing any inconvenience. We love Libya and we came here to film its struggle for freedom and report the news."
Former British ambassador to Libya, Sir Richard Dalton, told BBC Radio Wales that Press TV was a "genuine television operation", adding: "One might worry about its editorial decisions and some of the slants it puts on the news but I think it's easy for the British government to make the case that, prima facie, these people were there for their declared purpose."
Plaid Cymru MP for Carmarthen East Jonathan Edwards said: "The key point here is that we are not talking about spying - which was far, far more serious - as we were a few weeks ago. We're talking about entering the country illegally.
"They have already admitted that. I think there will be a deportation process and I'm hopeful that Gareth will be back in Wales very soon."