Bilgin says land has already been handed over to the consortium for the start of construction.
The extension is due to open in March 2018, offering a 46-minute journey time between the airport and Kadiköy.
Line M4 is the first metro line on the Asian side of Istanbul. The initial 21.8km phase from Kadiköy to Kartal opened in August 2012 and the 3.4km Kartal - Kaynarca section is currently under construction.
Istanbul Atatürk, the city's other international airport, has been linked to the metro network since the opening of the western extension of Line M1 from Yenibosna in December 2002.