Free and fair elections in Libya should be held "in the shortest possible time," United Nations special adviser on Libya Stephanie Williams said as she met with senior politicians and highlighted the need for calm.

Williams said on Twitter she met the prime minister of the Government of National Unity, Abdul Hamid Dbeibah, and also Fathi Bashagha, named by the east-based pro-putschist Gen. Khalifa Haftar parliament to head a new government in a process rejected by the incumbent prime minister.

The move threatens to spark a new power struggle between the eastern-based assembly and Dbeibah's administration based in Tripoli, in western Libya.

The tycoon, appointed a year ago as part of United Nations-led peace efforts, has vowed only to hand power to a government produced by the ballot box.

His administration had a mandate to lead the country to elections on Dec. 24, but they were canceled amid bitter divisions over their legal basis and the candidacies of several controversial figures.

Parliament Speaker Aguila Saleh, who like Dbeibah and Bashagha had been a presidential candidate, has since spearheaded efforts to replace the unity government.

The assembly had considered seven candidates to lead the administration, but shortly before Thursday's confirmation vote, Saleh had announced that Bashagha was the only remaining contender, when former interior ministry official Khaled al-Bibass had withdrawn from the race.

In a televised address on Tuesday, Dbeibah had vowed he would "accept no new transitional phase or parallel authority" and declared he would only hand over power to an elected government.

Both Bashagha and Dbeibah have the support of rival armed groups in the Libyan capital.

The U.N., Western powers and even some members of parliament have called for Dbeibah to stay in his role until elections, for which a new date has not yet been set.