The GNC, elected after the 2011 armed uprising that toppled autocratic leader Moamer Kadhafi, has stirred popular anger by extending its mandate from early February until the end of December.
Under pressure from demonstrators, the Congress, Libya's highest political authority, has announced that early elections will be held but without setting a date.
And yesterday dozens of them entered the General National Congress, with some of them rampaging through the building, witnesses said.
The protesters demanded the dissolution of the GNC and railed against the "kidnapping" overnight of demonstrators from a sit-in outside the parliament building.
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One member of the GNC said that the protesters, mostly young people armed with knives and sticks, entered the premises chanting "Resign, resign".
Media outlets said congressman Abdelrahman al-Swihli had been hit by a bullet while trying to flee the scene, but this could not be confirmed.
"Two (GNC) members were hit by bullets when they tried to leave the venue in their cars," Nuri Abu Sahmein, the speaker, told Al-Nabaa, blaming "armed protesters" for the shooting.
"Armed men came firing in the air and they set fire to a tent set up by demonstrators" in front of the GNC, said protester Milad al-Arbi.
Yesterday, residents blocked roads in the area to demand the release of those held, an AFP photographer said.
According to demonstrators, the gunmen belonged to the Operations Cell of Libyan Revolutionaries, a former rebel group which operates under the GNC's command.
It prompted the justice ministry to issue a brief statement denouncing the abduction "of youths who were expressing their views".