Mohamed al Shami, whose government is not recognised by the international community, said its forces pulled out late Thursday from the airport which had "fallen into the hands of the IS organisation".
He said the forces had pulled out of the airport, which is also a military base called Gardabiya, to redeploy "as part of an operation to secure" two areas east and west of Sirte.
It was the first time that IS in Libya has recorded such a military gain.
"After they left, Islamic State group fighters entered the base which had been completely emptied of equipment, except for one military plane which is out of use," said Shami.
Gardabiya is located 20 kilometres (12 miles) south of Sirte, hometown of late dictator Moamer Kadhafi who was ousted and killed in Libya's 2011 uprising.
Read: Battle for Libya airport leaves at least 47 dead
IS itself said it took full control of the airport following clashes with forces loyal to the Tripoli government, in a message posted on Twitter.
Sirte has been the scene of several months of sporadic fighting between IS and the Fajr Libya (Libya Dawn) militia alliance tasked by the Tripoli government to secure the city.
Shami said the pro-Tripoli forces would launch a counteroffensive to retake the airport once reinforcements arrived.
Sirte, 450 kilometres (280 miles) east of Tripoli, has been a bastion of extremism, with rival groups positioned in the Mediterranean city.
Since Kadhafi was toppled, chaos has gripped Libya as battle-hardened former rebel groups armed with heavy weapons carve out their own fiefdoms.
Fajr Libya seized control of Tripoli last year and set up a government and parliament opposed to the administration recognised by the international community that has taken refuge in the country's far east near the border with Egypt.
IS militants has exploited the chaos to gain ground, especially around Sirte, where it first emerged in February.
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