Ali Zeidan, a career diplomat and long-time Gaddafi critic, elected a week after the last prime minister was dismissed.
About 120 prisoners have escaped from a jail in the Libyan capital Tripoli, Khaled al-Sharif, National Guard chief, has told AFP news agency.
He said security services were on high alert to catch them.
Monday’s breakout comes less than a week before the October 20 first anniversary of former leader Muammar Gaddafi’s capture and death in his home town, Sirte.
“About 120 common criminals escaped from al-Jadaida prison today. Security services are on high alert to catch them,” Sharif said.
“We are trying to hunt them down and some have already been arrested.”
Earlier this year Libyan authorities took control of several prisons, including al-Jadaida, which were previously in the hands of former rebels who fought Gaddafi’s forces last year’s revolt that deposed him and in which he was killed.
The justice ministry controls al-Jadaida prison which is reserved for common criminals. In August there was a mutiny at the facility in which two inmates were hurt.
Rights groups have regularly denounced human-rights violations of leaders from the previous regime who are being held in prisons still under the control of former rebels.