Parliament unanimously chose a former interior minister, Fathi Bashagha, as the new leader of the Government of National Unity (GNU).
“The House of Representatives unanimously approved Fathi Bashagha to head the government,” the body's spokesman Abdullah Bliheg announced on Twitter.
But Mr Dbeibah insisted he will not leave office, saying he will remain until Libya holds elections. In televised comments, he said he would “accept no new transitional phase or parallel authority".
Mr Dbeibah’s decision leaves Libya at a political impasse. He was appointed prime minister by Parliament last year as head of an administration given the task of leading the country to elections scheduled for December 24.
Those elections were cancelled due to arguments over the constitution and the eligibility of several candidates.
Mr Dbeibah insists he should remain in office until those elections are held, but Parliament has called for a fresh constitutional process with elections to be held in 14 months’ time.
Mr Bashagha is officially prime minister-designate, as he has two weeks to form a Cabinet and have it approved by Parliament before officially taking office. Until then, Mr Dbeibah remains in power.
In the early hours of the morning, there were reports that Mr Dbeibah’s motorcade had been fired on in Tripoli in an apparent assassination attempt. Television footage showed a bullet strike on the window of a black vehicle he was said to be travelling in.
At the other end of the country, MPs gathered at the Parliament in Tobruk with confusion arising over whether Mr Bashagha's sole rival, Khaled Bibass, had withdrawn.
Reports after the vote claimed Mr Bibass had not withdrawn and that a fresh vote was needed, but Parliament spokesman Mr Bliheg insisted that the vote for Mr Bashagha was passed with “unanimous consent".
Mr Bashagha, 59, from the western city of Misurata, is a political ally of Parliament Speaker Agila Saleh.
In late 2020, the two men teamed up as candidates for prime minister and president of the GNU, respectively, but lost to Mr Dbeibah and his allies.
Mr Bashagha backed the 2011 rebellion that overthrew Muammar Qaddafi and was appointed interior minister in a previous government in 2018.
In recent weeks, he has pledged that, as prime minister, he would work to unify the country and raise the level of prosperity.
Mr Dbeibah, 62, also from Misurata, was appointed by Qaddafi to lead Libya’s powerful state-owned construction agency Libyan Investment and Development Company, responsible for key public works. He later became a prominent businessman and was appointed interim prime minister in the lead-up to the cancelled national elections.
Mr Dbeibah’s term in office has been stormy. He angered critics by standing in the cancelled December presidential election, despite previously pledging not to do so.
His oil minister, Mohamed Oun, repeatedly clashed with Mustafa Sanalla, head of state oil agency the National Oil Corporation, over control of the country’s petrochemicals industry, which accounts for about 95 per cent of Libya’s export earnings.
One bright spot has been that a ceasefire, negotiated in October 2020, has mostly held, although forces remain deployed near the central coastal town of Sirte. The UN has repeatedly called for 20,000 foreign mercenaries it estimates are in the country to withdraw.
But some fear that with both Mr Bashagha and Mr Dbeibah insisting they are prime minister, the country may return to the parallel governments that were formed with the start of the civil war in 2014.
With procedural arguments unlikely to be resolved, the rivalry between Mr Dbeibah and Mr Bashagha is likely to depend on who can draw support from Libya’s splintered political and military landscape, as well as which man the UN and outside powers decide to back.