* Lawmakers vote for immediate ceasefire
* Tripoli, Benghazi fighting worst since 2011 revolt
* Islamist deputies reject new House of Representatives
By Ayman Al-Warfalli and Feras Bosalum
BENGHAZI, Libya, Aug 6 (Reuters) - Libya's newly elected House of Representatives on Wednesday called for an immediate ceasefire under United Nations supervision to end three weeks of clashes among rival armed factions that have killed more than 200 people.
After the worst fighting in Tripoli and Benghazi since the 2011 uprising ousted Muammar Gaddafi, Western governments have mostly closed up their embassies, fearing the North African state is edging toward another civil war.
Lawmakers, meeting in the eastern town of Tobruk far from the clashes in Tripoli and Benghazi, on Wednesday voted to back a proposal for an immediate ceasefire that would be monitored by the United Nations.
Details of the proposal were not immediately available, and it was unclear warring militias would accept the parliament decision after some of their political allies had already dismissed the new 200-member Congress as unconstitutional.
"One hundred and thirty-one members of the parliament have voted to support an immediate ceasefire for all ongoing fighting in the country and to let United Nations supervise the operation," said lawmaker Iissa al-Oraybi.
Libya's western partners, who once backed the 2011 rebellion with NATO air strikes, hope the new assembly can end the political deadlock that triggered heavy clashes in the capital and the eastern city of Benghazi.
But the United Nations, the United States and most European countries have already closed up their embassies and evacuated staff. It was unclear whether the United Nations would accept any immediate role in monitoring.
The parliament also voted to hand some executive powers temporarily to the legislature until a new presidential election and a new president is chosen, as lawmakers push to consolidate their transition from a previous parliament.
Elected in June, the House of Representatives replaces the General National Congress (GNC) after a vote which, analysts said, eroded the dominance of Islamist factions linked to the Muslim Brotherhood in the legislature.
Some Islamist-leaning lawmakers and former GNC deputies allied with the Misrata armed brigades involved in Tripoli clashes have rejected the new parliament as unconstitutional.
On Wednesday, there was little of the heavy artillery and rocket fire that for the last three weeks has hit southern and western Tripoli, where Islamist-leaning Misrata brigades are fighting to take control of Tripoli airport from rival militias allied with the town of Zintan.
The battle for the airport is part of a wide struggle between two loose factions of ex-rebels and their political allies who once fought together against Gaddafi, but whose rivalries have erupted over dominations of postwar Libya.
On one side are the Zintan brigades - based in the city some 130 km (80 miles) southwest of Tripoli - with their anti-Islamist Qaaqaa and Al-Sawaiq fighters, including some ex-Gaddafi forces, and political allies who say they are a defending Libya against extremists.
Against them are fighters loyal to the western port of Misrata and other militias who are allied with the Islamist Justice and Construction party, an arm of the Muslim Brotherhood, who say they are fighting ex-Gaddafi elements. (Writing by Aziz El Yaakoubi; Editing by Patrick Markey and Gunna Dickson)