"The decision (to postpone) was made in the wake of listening to the pleadings of the defense panel that argued that this military court is not a competent entity and called for referring the case to the civil judiciary," LANA said on its website.
The prosecutors at the trial, which is being held at a military base in the eastern city of Benghazi, have accused the 41 men of murder and aiding prisoners to escape.
Intisar al-Agili, a Benghazi representative of the ruling National Transitional Council, told Reuters the trial had been postponed to February 15.
"The delay is based on the requests of the 15-lawyer defense team to review the evidence ... and on the requests of some detainees who want to hire their own lawyers," she said.
Libya is currently at loggerheads with the International Criminal Court (ICC), after militia fighters captured Saif al-Islam, Gaddafi's most prominent son, in November.
Libya says it will try Saif al-Islam at home, where he could face the death penalty. But the global court based in The Hague has said Libya will first have to answer concerns, raised by activists, that Saif al-Islam was being held incommunicado, without access to lawyers, and to provide information about his mental and physical health.
If the war crimes court rules Libya is unwilling or unable to try Saif al-Islam, who is accused of crimes against humanity over the killing of civilian protesters, it says it will take jurisdiction.
Saif al-Islam would rank among the biggest names to go before the ICC if he were transferred to The Hague for trial.
Writing by Oliver Holmes; Additional reporting by Marie-Louise Gumuchian in Tripoli; Editing by Sophie Hares