Erdogan was in New York to attend the annual UN General Assembly meeting, which he is scheduled to address on Tuesday.
Tesla currently has six factories, including two outside the United States – one in Shanghai focused on the Asian market and a second focused on European sales near Berlin.
It is also building one in Mexico and has tentative plans for a plant in India.
Erdogan likes to promote Türkiye’s high-tech sector, which is arguably most famous for its Bayraktar combat drones.
The drones, which helped Ukraine repel Russia’s march on Kyiv in the first weeks of its invasion last year, featured prominently during Erdogan’s May re-election campaign.
Türkiye this year also unveiled its first domestically-made electric vehicle, called Togg, which requires a constant stream of electric batteries and parts.
Musk’s SpaceX has also been working with Türkiye’s space industry, launching some of its communication satellites.
Erdogan’s office said he invited Musk to attend Teknofest, a technology fair scheduled for later this month in Türkiye’s western city of Izmir.