The parliament, elected June 25, is to take over from the interim General National Congress (GNC) chosen in the wake of the 2011 NATO-backed revolution that ousted longtime dictator Moamer Kadhafi.
It was to have convened in Benghazi on Monday, but the meeting was brought forward and shifted to Tobruk farther east for security reasons.
Both Benghazi and the capital, Tripoli, are the scene of regular fighting that has killed more than 200 people and wounded another 1,000 in the past two weeks.
Tripoli airport has stayed closed since gunmen, mostly Islamists, attacked it on July 13 in a bid to wrest control from the Zintan brigade of former rebels who have held it since the 2011 revolt.
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The brigade's opponents view it as the armed wing of the nationalist movement, and the battle is seen as part of a struggle for political influence as the new parliament prepares to assume office.
Ever since Kadhafi was ousted and killed, the new authorities have struggled in vain to rein in the many militias which have carved out their own fiefdoms and often clash.
There were no immediate reports of casualties.
A blaze at a fuel depot near the airport erupted last Sunday when a rocket hit a storage tank.
A civil defence official today reported progress in putting out the fire engulfing three tanks and threatening more than 90 million litres of fuel, as well as natural gas stocks.
But later a fourth tank was hit by a rocket and set ablaze, said Mohamed al-Hrari, spokesman for the National Oil Co.