* Says to visit OPEC member state as early as next week
* Libya torn by fighting between armed factions
* Fears of descent into outright civil war (Add protests in main Libyan cities)
By Patrick Markey
TRIPOLI, Aug 15 (Reuters) - - The new U.N. special envoy to Libya plans to visit Tripoli as early as next week to seek a ceasefire between armed factions whose clashes have turned parts of the capital into a battlefield, his office said.
Bernardino Leon aims to end fighting between brigades from Misrata and fighters allied to the western town of Zintan, whose rivalries erupted a month ago into the worst clashes since the 2011 uprising that ousted Muammar Gaddafi.
The battles, which involve brigades of former rebels who once fought Gaddafi together, have forced the United Nations and Western governments to evacuate their diplomats, fearing Libya is sliding into civil war.
A statement by his office said Leon's Tripoli visit for talks would be conducted with the United Nations as the only international mediator accepted by all Libyan parties.
"It is in this framework (that) I am planning to travel to Tripoli as early as next week to continue to support the talks between the parties," it said.
Most of the fighting has raged over the international airport in Tripoli, which fighters from Zintan have controlled since sweeping into the capital during the 2011 war.
Misrata and Zintan forces have exchanged barrages of Grad rockets, artillery fire and mortars across southern Tripoli, forcing hundreds of families from their homes and killing more than 200 people.
Libya's fragile government still has no national army and often put former rebels on the state payroll as semi-official security forces, as a way to co-opt them into the new state.
But the heavily armed rival brigades are allied with competing political factions and are often more loyal to their region, city or local commanders than to the Libyan central government.
"In my personal opinion, there are some urgent matters and a principle that should be agreed. The principle is that this should be a real ceasefire where ... I expect both sides to (both) talk in good faith and not to use it for military regroupment purposes," Leon said.
He said talks should address conflicts in other parts of Libya, the government control of airports with U.N. support, and the withdrawal of armed groups and their allies from Tripoli.
Several thousands people rallied in Tripoli, Benghazi, Misrata and other cities against the Congress, which has called on the United Nations to protect civilians.
Gunmen attacked protesters in Martyrs Square in downtown Tripoli, and police responded by opening fire, a Reuters reporter said. It was unclear if there were any injuries.
In a sign of deep polarisation, a group supporting both the parliament meeting in the eastern town of Tobruk and its decision to call on the United Nations intervention took to the streets in the city of Benghazi.
Islamist-leaning politicians and their allies from the city of Misrata describe the parliament's meeting as unconstitutional because it is taking place in Tobruk rather than Tripoli or Benghazi.
"We are protesting to express our complete rejection to any foreign intervention in Libya wanted by the House of Representatives," said Imad Shanib, one of the Tripoli protest's organizers.
A separate battle in the eastern city of Benghazi has complicated Libya's security, with an alliance of Islamist militants and ex-rebels forcing the army out of the city.
Three years since the Gaddafi's one-man rule ended, Libya's fragile efforts towards democracy are close to chaos. Rival brigades often stormed the last parliament to pressure lawmakers. The month of fighting in Tripoli and Benghazi has further polarised the political factions and their militia allies. (Additionnal reporting by Ahmed Elumami and Ayman El-Warfalli in Benghazi, Heba Alshibani in Tripoli. Writing by Patrick Markey and Aziz El Yaakoubi.; Editing by Mark Heinrich, Larry King)