Haftar has vowed to "liberate" Derna, an Islamist stronghold that is home to more than 120,000 people and the only eastern city outside of his control.
But as his self-styled Libyan National Army continued its offensive on Tuesday, two explosions were heard as suicide bombers hit forces in the southern Shiha district.
Without giving a toll for the attack, LNA spokesman Khalifa al-Abidi said civilians were among the casualties as the roof of a family home collapsed.
On Monday night, he said, another suicide attack killed two LNA fighters and wounded three.
The LNA was "advancing steadily to liberate a very small remaining pocket before liberating the whole of Derna," he added.
Abidi said "terrorists" were "resorting to suicide attacks after they failed to tackle" the LNA conventionally.
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 city is located more than 1,000 kilometres (600 miles) east of the capital Tripoli and around 300 kilometres east of second city Benghazi.
- Brink of 'humanitarian catastrophe' -
Haftar has struggled to succeed in the fight against insurgents, according to Federica Saini Fasanotti from the Brookings Institution in Washington.
"I am not sure that this operation will bring a quick victory for him in military terms. In social terms it is already a disaster," she said.
Since the start of the offensive on May 7, residents have faced food and medicine shortages, as well as cuts to electricity, water and phone lines.
Abdessalam al-Hassi, leading operations in Derna, said supplies were being dispatched to "liberated zones".
An LNA victory in the city was "only a question of time", Hassi said.
The Red Cross said it has sent aid to 6,000 people in the neighbourhood of Bab Tobruk, as well as to thousands of others who have fled the city to seek refuge in the surrounding areas.
Amnesty International has called on all sides to let relief into the city and allow civilians to leave "without fear of arbitrary detention, harassment, intimidation and unlawful killings".
"We are receiving horrifying reports from Derna, where a prolonged siege and heavy fighting have left the city on the brink of a humanitarian catastrophe," said Heba Morayef, the organisation's Middle East and North Africa director.
Haftar joined rival Libyan leaders last month in Paris, where they agreed to prepare for polls in December.
For Saini Fasanotti, the LNA chief would do better to sideline his military ambitions.
"I think that he should start to focus on a political campaign for the elections," she said.
Haftar supports an administration based in the east, which opposes the internationally recognised government in Tripoli.
The strongman's critics accuse him of wanting to establish a military dictatorship and say he is supported by foreign forces from Egypt, the United Arab Emirates and France.