Haftar is campaigningto rid Libya of fighters that he says the weak central government has failed to control.
Suleiman El Dressi, a Benghazi resident in the area of the clashes, told Al Jazeera that two people had been killed as a result of explosions there.
"Residents are at home and they are very scared, waiting for the clashes to be over," he said.
"Central government cannot control anything happening here, in the east [of the country], they are useless."
On Sunday, a Libyan fighter jet under Hafter`s command has attacked an Ansar al-Shariah base in Benghazi but did not hit the target, witnesses and a senior Libyan official told agencies.
The Associated Press news agency cited a member of Ansar al-Shariah as saying no one was hurt in the bombing.
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