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US war planes launched air raids for the second day in the row in Libya on the Islamic State group's bastion in the war-torn country.

Sirte on the Mediterranean coast has become the base for IS militants in Libya since last year.

But the jihadi group's hold over the city now looks to be loosening as militants as pro-government forces close in backed by US air power.

Forces loyal to the Tripoli-based Government of National Accord gained full control of al-Dollar, a central residential district in Sirte after losing five men on Tuesday.

US aircraft war planes launched five air strikes on Monday against "several targets in Sirte, hitting IS members and vehicles", the GNA forces said in a statement.

On Tuesday, the US launched two more raids on Sirte. Washington said the unity government led by Fayez al-Sarraj requested the air strikes, which is leading the fight against IS.

"It is in America's national security interest in our fight against [IS] to make sure [the GNA are] able to finish the job," President Barack Obama said on Tuesday.

"We're working in partnership with them to assure that IS does not get a stronghold in Libya, even as Libya begins what is going to be a long process to establish a functioning government and security system."

Among the targets of US missiles were two T-72 tanks, and a number of IS militants killed.

The bombings on Monday were the first by the US in Sirte itself.

The GNA press office said Tuesday that the latest strikes had destroyed an IS rocket launcher and a vehicle.

More than 300 pro-government fighters have been killed and over 1,500 wounded during the battle for Sirte with a breakthrough made in June when GNA forces entered the city.

Sarraj said US involvement would be "limited in time and will not go beyond Sirte and its suburbs".

The Libyan parliament in Tobruk which has been fighting a war for control of the country with the Tripoli government branded the US strikes a "violation of (Libyan) airspace".

Meanwhile, a suicide bomber killed at least 15 soldiers loyal to the non-recognised government in an attack in the eastern city of Benghazi claimed by a militia alliance, the Revolutionary Shura Council.

Agencies contributed to this story.