* Crude output slips for first time since port deal
* Fresh clashes in Tripoli and Benghazi
* Brega oil port seen open in few days (Recasts with suicide attack)
By Ayman al-Warfalli and Ahmed Elumami
BENGHAZI, Libya, July 22 (Reuters) - A twin suicide bombing at a Libyan army base in Benghazi killed at least four solders in an escalation of clashes between Islamist militants and regular forces battling to oust them from the eastern city.
A first attacker blew himself up at the entrance to Benghazi's special forces headquarters, allowing a second suicide bomber to detonate his explosives at the base and kill at least four troops, a security source said.
Suicide bombings are rare in Libya, where a fragile government is struggling to impose order. Tripoli and Benghazi are now caught up in some of the fiercest fighting between rival armed groups since the fall of Muammar Gaddafi in 2011.
In another blow to the government, Libya's oil production has fallen, turning back a hard-won increase since April in revenue for the state just as it faces increased fighting around the airport in the capital and across Benghazi.
More than 40 people have died in a week of fierce clashes at Tripoli airport involving artillery, Grad rockets and anti-aircraft guns.
Fresh fighting broke out overnight on Monday in Tripoli and also Benghazi. In the eastern city, armed regular forces and troops loyal to a renegade former army general are battling Islamist militants who have entrenched themselves there.
Beyond the suicide blast, there were no immediate reports on casualties from Monday's fighting in Benghazi or the Qasr Ben Ghashir neighbourhood near Tripoli airport where residents have been forced from their homes or trapped by the gun battles.
"There are a lot of families still stuck and not able to get out because of the intensity of the shelling and bombing, which is with all kinds of heavy weapons," said local area mayor Mohammad Abdullah.
The clashes have prompted the United Nations to pull its staff out of Libya, stopped most international flights and damaged more than a dozen planes parked at the airport.
One local airline's Airbus jet billowed black smoke after being hit on Monday.
The airport clash reflects national divisions between two increasingly polarised factions whose battle is shaping the future of Libya's transition since the 2011 revolution ended four decades of Gaddafi's one-man rule.
One side is grouped around the western town of Zintan and their allies who are loosely tied to the National Forces Alliance political movement.
The other faction centres on the more Islamist-leaning Misrata brigades and allied militias who side with Justice and Construction Party, a wing of the Muslim Brotherhood.
Egypt's Foreign Ministry warned its citizens on Tuesday not to travel to Libya after 22 Egyptian soldiers were killed by gunmen near the border on Saturday.
"In the light of escalating violence... on Libyan soil, especially in Benghazi... the Egyptian Foreign Ministry calls on all citizens not to travel at all to Libya at the current time for their own safety," it said in a statement.
FALLING OIL REVENUES
Libya's oil resources have often been targeted by armed groups since 2011 to push the government for financial or political gain. Last year a string of protests slashed oil output to less than half the usual 1.4 million barrels per day.
A negotiated deal in April mostly ended a year-long blockade by a former rebel commander over four key oil ports, allowing Libya to slowly rebuild production, shipping crude and earning vital oil revenue.
But those gains seemed to have been eroded by the growing violence. The El-Feel oilfield last week was forced to cut back due to clashes in Tripoli, where the two rival brigades of militias have fought over control of the airport.
El-Feel, operated by state-run National Oil Corporation and Italy's ENI, is protected by security guards from the northwestern Zintan region, whose fighters also protect the airport where clashes have gone on for a week.
National Oil Company spokesman Mohamed El Harari said output as of Monday was around 450,000 bpd compared with 555,000 bpd on Thursday.
Still, oil industry progress remains in flux. One of Libya's ports, Brega, is expected to be operating within a "few days" after the government reached a deal with protesting security guards to end a blockade, NOC's Harari said.
According to Reuters AIS Live tanker tracking service, no tankers had loaded so far at Brega. One crude shipment left the 230,000 barrels-per-day Zawiya port, supplied by the El Sharara oilfield, which was recently reopened.
The Olympic Spirit II, carrying Aframax, crude oil, headed to the Spanish port of Bilbao having left July 20. (Reporting by Tripoli newsroom and Feras Bosalum in Benghazi; Writing by Patrick Markey; Editing by Tom Heneghan)