JAKARTA, Indonesia — One resort, planned as the largest in Bali, will overlook a spectacular Hindu temple. The other, in the verdant hills of West Java, will adjoin a theme park. The properties will be so luxurious, the Trump Organization says, that even an impressive five-star rating will not do them justice. So it will give them six stars instead.

Even as President-elect Donald J. Trump promises to end foreign business deals that could pose conflicts of interest — there will be “no new deals” while he is in office, he has said — his company is moving ahead with two Indonesian projects that illustrate how tricky that pledge might be.

None of the construction work to build or renovate structures at the Indonesian resorts has even begun, but Mr. Trump has forged relationships with powerful political figures in Indonesia, where such connections are crucial to pushing through big projects.

That tangle of relationships includes an Indonesian business partner who aspires to high office; a powerful politician accused of trying to extort billions of dollars from an American mining company; as well as Mr. Trump’s adviser on regulatory issues, Carl C. Icahn, who is a top shareholder in the same mining company.