* Election proposal seen to defuse militia tensions
* Parliament chief calls for Misrata brigade support
* US says does not back Haftar actions in Libya (Adds Pentagon comments, paragraph 13)
By Ahmed Elumami and Ulf Laessing
TRIPOLI, May 20 (Reuters) - Libyan authorities on Tuesday proposed a June national election as the government sought to resolve a standoff over parliament involving powerful brigades of former rebel fighters.
Libya's General National Congress (GNC) is at the heart of the crisis after gunmen claiming loyalty to a renegade former general attacked the parliament with anti-aircraft cannons on Sunday, demanding its suspension.
Parliament, split between Islamist and anti-Islamist forces, had said in February it would hold early elections, under pressure over Libya's chaotic transition to democracy since the 2011 uprising that ousted Muammar Gaddafi.
The June 25 election proposal appeared to be an attempt to ease tensions after Sunday's attack claimed by forces loyal to former General Khalifa Haftar, and to avoid the potential response by rival Islamist militia brigades.
"The commission has not yet officially announced June 25 as the date of the elections of the House of Representatives. But it is only one of the proposals to hold the elections," election commission member Abdulhakeem Al-Shaab told Reuters.
A local television station had earlier quoted the election commission saying that the June date was set.
In some of the worst fighting in Tripoli since the 2011 war, gunmen shelled the General National Congress on Sunday in an attack claimed by forces loyal to Haftar, who has begun a campaign to purge the North African country of Islamists.
Three years after the end of Gaddafi's one-man rule, Libya remains in constant upheaval, its government fragile, parliament split and the nascent army unable to control rival bands of former rebels who often challenge the state.
A former Gaddafi ally who split with the autocrat in the 1980s, Haftar is the latest player to emerge in Libya's network of ex-fighters, militias and Islamist militants vying for control over parts of the country.
Haftar's troops on Friday attacked Islamist militants in Benghazi in the worst clashes in the eastern city for months, killing more than 70 people. His allies say he wants to purge the country of Islamist militants.
The parliament itself is split between Islamist parties loosely allied to the Muslim Brotherhood, the anti-Islamist National Forces Alliance, and scores of independents and tribal leaders of varying allegiances.
The United States has temporarily moved about 250 Marines and a number of aircraft to Sicily from Spain as a precaution due to concerns about Libya's turmoil, strengthening the U.S. ability to evacuate its citizens.
"We're watching (the situation) very closely. It's certainly unsettling," said Pentagon spokesman Rear Admiral John Kirby, adding the Marines were "ready to go, if they're needed."
The U.S. State Department said on Tuesday it does not endorse Haftar's actions and called for dialogue to end the unrest in the North African oil-producing state.
"We have not had contact with him recently. We do not condone or support the actions on the ground, nor have we assisted with these actions," spokeswoman Jen Psaki told reporters. "We are continuing to call on all parties to refrain from violence and to seek resolution through peaceful means."
Haftar has gained support from some regular army units and his forces claim backing from the Qaaqaa and Sawaiq militias who are fiercely anti-Islamist. But his movement may goad rival Misrata brigades and Islamist militia into reactions.
Libya's parliament moved to a luxury hotel on Tuesday until the powerful militia from the western city of Misrata can take up positions to protect its old building, a parliamentary spokesman said.
Western governments fear Haftar's campaign may split the Libyan army, further destabilising the country, after several units defected, including a special forces brigade chief and air force elements in the east.
Another former rebel who is supporting Haftar is Ibrahim Jathran, whose forces have closed off key Libyan oil ports since summer, cutting into vital crude shipments. He is demanding more federal autonomy for his eastern region.
Tripoli was calm on Tuesday, but diplomats say the involvement of Misrata militia opposed to Haftar's attempts to force an anti-Islamist alliance may create new tensions.
The Muslim Brotherhood have strong roots in Misrata and are rivals of a militia from Zintan in the western mountains, which controls part of Tripoli and which some officials have blamed for the attack on the parliament.
Parliamentary spokesman Omar Hmeidan said speaker Nuri Abu Sahmain had asked a Misrata force to secure parliament's premises.
"The Congress decided to hold today's session in a hall of the Radisson Blu hotel until the Central Shield force from Misrata finishes preparations to start securing the headquarters of the parliament," he said.
Parliament had planned to discuss approving a cabinet for newly appointed prime minister Ahmed Maiteeq, but postponed debate as it lacked a quorum, he said.
The appointment of Maiteeq, who is from Misrata and is Libya's third prime minister since March, has angered people in the east because he is supported by the Muslim Brotherhood and is seen by critics as pro-Islamist.
(Writing by Patrick Markey and Ulf Laessing; Editing by Mark Heinrich and Gunna Dickson)