The explosions were heard across Derna as the bombers hit the Chiha district in the south of the town, spokesman Khalifaal-Abidi said.
Abidi did not give a toll for the attacks but said the roof of a family home collapsed.
On Monday night, another suicide attack killed two fighters of Haftar’s Libyan National Army [LNA] and wounded three, the spokesman said.
Over the past month, the self-styled LNA has been engaged in an offensive to take Derna, the only eastern town outside Haftar’s control, which is home to about 150,000 people and held by hardline fighters since the uprising that ousted dictator Muammar Qaddafi.
Derna is held by a ragtag alliance of Islamist and jihadist militias, including groups close to al-Qaeda, hostile to both Haftar and the Islamic State group.
The coastal town is located more than 1,000 kilometres (600 miles) east of the capital Tripoli and around 300 kilometres east of second city Benghazi.
Abidi said the LNA is “advancing steadily to liberate a very small remaining pocket before liberating the whole of Derna.”
He said “terrorists” were “resorting to suicide attacks after they failed to tackle” the LNA conventionally.
On Sunday, the Libyan Red Cross said it had delivered humanitarian aid to 6,000 people in western Derna’s Bab Tobruk district, in addition to thousands of others who have fled fighting in the embattled city to nearby areas.
LNA forces have besieged the city for nearly two years, making it difficult for residents to access humanitarian aid.
Libya has been wracked by chaos since the 2011 uprising that toppled and killed long-time dictator Qaddafi, with two rival authorities vying for control.
Haftar, whose forces are backed by the United Arab Emirates and Egypt, supports an administration based in the east which opposes the internationally recognised government in Tripoli that has so far struggled to assert its authority outside the west.
The strongman’s critics claim he wants to establish a military dictatorship.