DALLAS — Before taking office, Donald J. Trump pledged that his business empire would forgo new deals abroad while he was president. But as the Trump Organization unveils a new brand of hotels, that promise is not preventing the company from bringing foreign deals home.

The company, now largely run by Mr. Trump’s eldest sons, Eric and Donald Jr., has been pursuing a downtown Dallas hotel project with a real estate firm that has deep Turkish roots. The hotel, if built, would fall under the Trump Organization’s Scion chain, a more affordable alternative to its five-star luxury line.

An examination by The New York Times of records including corporation registrations, private emails and archived websites found that Alterra Worldwide, the real estate firm that would own the hotel and be partners with the Trumps, has business ties in Russia, Kazakhstan and at least two dozen other countries. Ordinarily, such international experience would be a selling point for the firm, but it is a complicating factor when dealing with Mr. Trump’s company, where concerns already have been raised internally about some of Alterra’s foreign connections.

These revelations show that as the Trump Organization rolls out its new hotel line across the country — properties that the Trumps will manage and their partners will own — a partnership with Alterra may invite the foreign entanglements and potential conflicts of interest that the company said it sought to avoid in its international dealings.