Erdogan asked Musk during a meeting at Turkish House, a skyscraper near the United Nations in New York, the Turkish news agency said on the social media platform X on Sunday.
Erdogan is in the United States to attend the 78th session of the United Nations General Assembly.
Musk is also set to meet Israeli Prime Minister Benjamin Netanyahu in California on Monday. Musk posted on X that their talks would focus on artificial intelligence technology.
Tesla in August expressed an interest in building a factory in India that would produce a low-cost electric vehicle (EV).
Tesla currently has six factories and is building a seventh in Mexico’s northern Nuevo Leon state, part of the electric carmaker’s push to expand its global footprint.
Musk said in May that the automaker would probably pick a location for a new factory by the end of this year.
Tesla shares are up 123 percent so far this year and the automaker on Saturday said it had produced its five-millionth car.
In addition to running Tesla, Musk also bought X, formerly known as Twitter, for $44bn in 2022.
While describing himself as a free speech absolutist, Musk has complied with some demands by the Turkish government to censor content in the country.
In other cases, the social media company has objected to orders by the Turkish courts.
