The Islamic State of Iraq and the Levant (ISIL) has claimed a suicide bombing that killed seven people in Libyan city of Benghazi, on the same day the UN proposed a six-point proposal aimed at ending the conflict.

Tuesday's deadly attack triggered retaliatory air strikes on suspected ISIL positions by army forces, said Naser al-Hasi, a spokesman for the military base in Benghazi.

A car laden with explosives drove into an army checkpoint in the Lithi district of Benghazi, where army officials say ISIL fighters are holed up. Five of those killed were soldiers, the other two civilians, army officials said.

Benghazi is suffering heavy clashes almost daily between ISIL and forces of the internationally recognised government. The port has been closed for more than four months, disrupting wheat and food imports.

In a separate incident in Libya's second-largest city, a rocket hit a residential building, killing a 17-year old girl and another person, medics said.

The latest violence comes after armed group Ansar al-Sharia said in a statement that a senior commander, Mohamed al-Areibi, had been killed in Benghazi on Monday.

The violence in Benghazi typifies chaos in Libya where two rival governments and parliaments allied to armed factions are competing for power four years after the ousting of Muammar Gaddafi.

Presidential council

The UN has been mediating to encourage the formation of a unity government in the north African country.

Envoy Bernardino Leon, who has been shepherding peace talks between Libya's rival parliaments, presented what the UN mission (UNSMIL) described as the "basis from which the parties can work" towards a solution.

The proposal was delivered at meetings in Tripoli and Tobruk, where the rival parliaments are based.

The UN proposed a council headed by a president and including two deputies and "independent personalities not belonging to any party or affiliated with any group," UNSMIL said in a statement on Tuesday.

Source: Reuters