Maitiq took his oath before President of the Parliament Nuri Abu Sahmain. He will wait for acting Prime Minister Abdullah Thinni to hand over his power, Xinhua quoted the official LANA agency as saying.
Maitiq, a businessman educated in Britain, won a confidence vote in parliament on Sunday after gaining 83 of the total 93 votes. But some politicians immediately challenged him, calling the vote "meaningless" as only 93 of the 200 lawmakers attended it.
Earlier on Monday, First Deputy President of the Parliament Ezzedine Awami made a statement saying the vote procedures were not legitimate and Thinni will stay as country's prime minister.
Awami said that his statement is in accordance with an announcement by the ministry of justice which also called the vote invalid.
The Libyan parliament has been stuck in a deadlock between the secular groups and Islamists since the 2011 popular protests that toppled the country's former leader Muammar Gaddafi.