Powerful militias made up of former rebels from the western town of Zintan had given the General National Congress, the country's highest political authority, Tuesday's deadline to quit, threatening to seize any lawmaker who ignored it.
Zeidan on Tuesday said the deadline had been extended by 72 hours but did not give further details of the compromise, telling journalists only that "wisdom has prevailed" after discussions with representatives from the militias, the assembly and UN.
The potential crisis arose exactly three years after the start of the Arab Spring uprising that toppled dictator Moamer Kadhafi but left the sprawling North African country with a weak central government that has struggled to impose order on former rebel brigades.
Commanders of the Zintan militias had in a televised statement said that they were giving the assembly five hours, until 1930 GMT, to "hand over power", pointing to a February 7 end of its mandate that it had extended.
"Any member of Congress who stays will be... a legitimate target and will be arrested, then judged," they said.

However the deadline passed with no action taken by the militias, and Zeidan, who himself was kidnapped and briefly held by armed men last year, announced the enigmatic "compromise".
The ultimatum had triggered a meeting between the head of the UN mission to Libya, Tarek Metri, and the militias' commanders. "I asked them to give a chance to political dialogue on the basis of general elections being held," Metri said.
The speaker of the General National Congress, Nuri Abu Sahmein, had earlier rejected the militias' ultimatum, calling it "a coup d'etat".

He said the army had been ordered to act against the militias, though no unusual troop movements were observed in the capital Tripoli following the video threat.
The Zintan militias issuing the ultimatum included the Al-Qaaqaa and Al-Sawaiq brigades, two of the most powerful and well-disciplined militias in the country, both nominally loyal to the regular army.
Zintan, in the mainly Berber highlands southwest of Tripoli, was one of the bastions of the NATO-backed uprising that ended the four-decade rule of Kadhafi, who was captured and killed by rebels.


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