A video released by the interior ministry showed rescue personnel tied to safety ropes climbing into cabins.
They hope to complete the rescue work before sunset on Saturday.
A group of 10 opposition MPs were also headed to the scene to “investigate the accident in detail,” said Ozgur Ozel, chair of the opposition Republican People’s party.
Turkish prosecutors have launched an investigation and ordered the detention of 13 people in relation to the incident, including officials from the private company running the cable car, Tunc Yilmaz, Turkey’s justice minister, told reporters after the rescue.
The Antalya Cable Car offers panoramas of Antalya and the Mediterranean Sea by taking passengers up over 1,500 metres to the top of Tunektepe.
According to its website, the cable car has 36 cabins with a capacity of six people each. The journey takes around nine minutes.
