The current violence pits Haftar's self-styled Libyan National Army, which backs a rival government in the east of the country, against an array of militias that support the Tripoli administration.
Haftar's forces, which control swathes of the country's east, launched an offensive earlier this month to take the Libyan capital, defying global calls to halt their battle against fighters loyal to the UN-backed Government of National Accord based in Tripoli.
While some pro-Haftar media had predicted a quick victory, Tripoli government forces have halted him about 11 km (7 miles) from the center near an airport that was largely destroyed in a previous bout of fighting five years ago.
No other details were immediately available.
In a sign of growing escalation, LNA jets have bombed the capital, including a school playground.
"Haftar's warplanes have been targeting several locations in and around Tripoli and also warplanes with the GNA have been targeting Haftar's locations south of Tripoli", Abdelwahed said.
The army, led by General Khalifa Haftar, is allied with the eastern-based government, as the country is politically divided between western and eastern governments.
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Earlier this week, the United Nations said the fighting had displaced more than 8,000 people.
The situation remained "very tense" on Tripoli's southern outskirts, Abdelwahed said, with the mass displacement constituting a "crisis" for authorities attempting to rehouse those forced to flee.
The meeting was scheduled to bring Haftar and al-Serraj together in the southwestern town of Ghadames on April 14-16.
Fighting in Tripoli has killed 121 people and wounded 561 since commander Khalifa Haftar launched an offensive earlier this month to take the Libyan capital, the World Health Organisation said Sunday.
Haftar will ignore calls for peace and continue his bloody offensive on Libya's capital.
"The president (Sisi) affirmed Egypt's support in efforts to fight terrorism and extremist militias to achieve security and stability for Libyan citizens throughout the country", according to a statement by the Egyptian president's office. "No matter how obstinate one becomes, there is no solution except a political one", Ghassan Salame said in a Twitter post.