"Our forces have won ground... and have successfully retaken important positions, including the air force academy," said Mustafa al-Mejii, a spokesman for forces loyal to the Tripoli-based Government of National Accord.
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He said the gains were made in Esbea sector, some 40 kilometres (25 miles) south of the capital.
Haftar's forces said in a Facebook statement that they had repulsed a GNA attack, inflicting "significant losses", without giving further details.
Haftar launched an offensive to take Tripoli, the seat of the GNA, in early April.
But counterattacks by forces loyal to the unity government led quickly to a stalemate in the southern outskirts.
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Mejii said that pro-GNA forces killed 20 of Haftar's fighters and wounded dozens of others on Wednesday.
He said seven pro-GNA troops were killed.
The fighting has displaced some 120,000 people since April, according to the World Health Organization.
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