This took place in the east as the European Union was considering sanctions on people obstructing U.N.-brokered peace talks.
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The United Nations had planned to hold this week a second round of talks to end a confrontation between two rival governments and parliaments but said a military escalation was undermining its efforts.
On Monday, a force allied to the rival assembly based in Tripoli, the General National Congress (GNC), moved to the east to try seize the Es Sider and Ras Lanuf oil ports. Both terminals have closed, drying exports of an estimated 300,000 barrels a day of oil.
The recognized government, forced to work out of the east since losing control of Tripoli in August, launched more air strikes on the rival forces positioned near Es Sider, eastern officials said.
They also said the rival force had for the first time used a jet to support its troops, though its spokesman Ismail al-Shukri denied this.
"We confirm the campaign will continue," Shukri told reporters, adding that oil facilities would not be harmed.
GNC spokesman Omar Hmeidan said the assembly was supporting the U.N. talks but said the venue needed to change and talks should reflect that the GNC was the legitimate body.
"Members of the GNC will attend the talks as representatives of the legislative body," he said, proposing to hold the next round in the southern town of Hun.
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The House of Representatives, the legislature aligned with recognized Prime Minister Abdullah al-Thinni, said in a statement it was supporting the U.N.-led dialogue but rejected talks with GNC members and its armed factions.
The U.N. had held a first round of talks in September in the southern city of Ghadames by inviting the House of Representatives and members from Misrata, linked to Libya Dawn, which has boycotted sessions.
U.N. Special Envoy Bernadino Leon said last week the next round would include GNC members. The U.N. has not given a date or venue, saying on Monday only talks would hopefully start "soon".
The European Union is ready to consider sanctions on people obstructing a political solution, EU foreign policy chief Federica Mogherini said.
"They must face consequences for their actions. The EU ... remains ready to consider further actions, including restrictive measures, should circumstances so require," she said in a statement.
Separately on Tuesday, African leaders meeting in Dakar urged western nations to act to resolve the crisis in Libya, which has sent shock waves across the vast arid Sahel band and threatened to destabilise fragile regional governments.