Erdogan urges Musk to build a new Tesla facility.

Erdogan and Musk have held a string of meetings both in Turkey and on the sidelines of international forums, developing a seeming friendship that they extended on Sunday in New York.

Turkish television on Monday showed Musk entering New York's Turkish House, a new skyscraper across from the United Nations building, with his three-year-old son, whom he held on his lap during the talks.

"President Erdogan called on Tesla to establish its seventh factory in Turkey," the Turkish leader's office said.

Turkey's Anadolu state news agency said Musk told Erdogan that his country was "among the most important candidates" for the new factory.

Erdogan's lobbying efforts follow those undertaken by French President Emmanuel Macron, who met Musk in June, and Spanish Prime Minister Pedro Sanchez.

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 Turkey'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.

Turkey 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 Turkey'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 Turkey's western city of Izmir.

But while cordial and full of laughs -- Erdogan presented a football to Musk's son, whom he and Canadian pop star Grimes named "X AE A-12" -- the meeting got off to a slightly awkward start.

"Where is your wife?" Erdogan demanded in English, a language that he rarely speaks in public.

"Oh she's in San Francisc," Musk said with a slightly nervous laugh. "We're separated and I take care of him mostly," he added, nodding at his son.

Musk and Grimes separated two years ago.

The 52-year-old tycoon was also married twice to the British actress Talulah Riley, and once to the Canadian author Justine Wilson.