Libyan authorities vowed Monday to stick to the "democratic path" in the face of mounting lawlessness in which two MPs were shot when protesters stormed the country's transitional parliament.

On Sunday, two members of the General National Congress (GNC) were shot and wounded as armed protesters stormed their building in Tripoli. In a separate incident, a French engineer was killed in the restive eastern city of Benghazi.

"I assure you we are committed to the path of the February 17 revolution and to pursue the democratic process," GNC president Nuri Abu Sahmein said in a televised address, referring to the uprising that ended Moamer Kadhafi's four-decade rule.

Abu Sahmein said the MPs' wounds were not life-threatening but condemned what he termed a "flagrant aggression on the seat of legitimate sovereignty."

He urged former rebel fighters who ousted and killed Kadhafi to protect the capital and state institutions.

On Monday, ex-rebels equipped with pick-up trucks mounted with anti-aircraft guns were posted around the GNC building, where at least five burnt-out cars testified to the previous day's violence.

Abu Sahmein said the GNC was examining a roadmap for the handover of power "as quickly as possible" to an elected body.

The GNC, elected after the 2011 uprising, has stirred popular anger by extending its mandate from early February until the end of December.

Under pressure from demonstrators, the GNC, Libya's highest political authority, has announced early elections will be held but has not yet set a date.

Dozens of armed demonstrators, some of whom rampaged through the building, on Sunday demanded the GNC be dissolved and railed against the "kidnapping" the previous night of participants in a sit-in protest outside the parliament building.

They later attacked and "abused" deputies, GNC spokesman Omar Hmidan said, adding that their cars had been destroyed.

One GNC member told AFP that the protesters, mostly young people armed with knives and sticks, entered the premises chanting "Resign, resign".

Two members were "hit by bullets when they tried to leave the venue in their cars," according to Nuri Abu Sahmein.

In Benghazi meanwhile, gunmen on Sunday shot dead a French engineer who worked for a company doing extensive work at a medical centre in the eastern city, which was the cradle of the 2011 revolt.

Three years after the uprising, the government and GNC have come under increasing criticism from Libyans who accuse them of corruption and failing to provide security.

Criminals roam the streets, and rival tribes shoot it out to settle long-standing disputes, while many ex-rebels have formed powerful militias rather than integrate into the regular armed forces and police.

The wave of lawlessness that since Kadhafi was captured and killed in October 2011 has seen militants mount near daily attacks on security forces and foreign missions, particularly in the east of the country.

An assault on the US mission in Benghazi in 2012 killed the ambassador and three other Americans.

And protesters have blockaded and shut down Libya's oil terminals, threatening to bankrupt a government that relies almost exclusively on petroleum revenues to operate.