Libya parliament agrees to "early" election amid public anger
* Ordinary Libyans weary of parliamentary infighting
* Libyans due to vote for body to draft new constitution
* Timing of next election remains unclear
TRIPOLI, Feb 17 (Reuters) - Libya's parliament will call elections "as early as possible", its president said on Monday, in an apparent effort to assuage ordinary Libyans angry over political chaos in the country nearly three years after the fall of Muammar Gaddafi.
The parliament, the General National Congress (GNC), is deadlocked between Islamists and nationalists, compounding a sense of chaos as Libya's fledgling army tries to assert itself against unruly ex-rebels, tribal groups and Islamist militants.
Many people in the OPEC oil-producing nation blame mainly the GNC infighting for a lack of progress in the transition towards democracy since the ousting of Gaddafi in 2011.
"The GNC announces... that elections will be held as early as possible," GNC President Nouri Abusahmain said in a televised speech marking the third anniversary of the start of the NATO-backed uprising against Gaddafi.
An election law will be approved by the end of March, he said, without providing a more precise timetable.
Tensions have increased over the GNC's own role after its initial mandate ran out on Feb. 7. Deputies agreed to extend their term in office to allow a special committee time to draft a new constitution but their move has sparked protests.
Libyans are due to vote on Feb. 20 for the body to draft the constitution. It will have 120 days to complete its task and it was not immediately clear whether the promised election would only take place after that period.
If successfully agreed, a new constitution would be a rare bright spot in a transition so far marred by instability and violence.
The GNC is deeply split between the nationalist National Forces Alliance party and the Islamists of the Justice and Construction Party, which is tied to the Muslim Brotherhood, and the Al Wafaa movement.
Oil production, Libya's lifeline, has slowed to a trickle as armed protesters and tribesmen have seized oil ports and fields across the vast desert nation to press political and financial demands. (Reporting by Ulf Laessing and Feras Bosalum; Editing by Gareth Jones)