At Trump Towers Pune, which were completed a few years ago as the first project in India to bear the Trump name, only seven of 46 units are occupied, according to building employees and others with knowledge of occupancy and sales.

The real estate market is now so weak, the Trump family’s partners in Pune decided to not even attempt — at least for now — to sell half of the luxury apartments in the complex, which retail for about 35 percent more than comparable properties.

Pune, Mumbai, Kolkata and Gurugram, a tech hub near New Delhi, all have Trump-branded projects. The deals in India were negotiated before Mr. Trump was elected, and the Trump family said they were contractually obligated to see them through. But the decision to push ahead has generated conflict-of-interest questions about the mixing of presidential duties with family business.

Panchshil Realty, which built the towers in Pune, did not answer emailed questions. Through a spokesman, the company’s chairman, Atul Chordia, declined to comment.

Asked to comment on its projects in India, the Trump organization and one of its India-based partners did not dispute that their real estate projects in India, particularly in Pune and Mumbai, have faced challenges because of the downturn in the luxury real-estate market.

But they argued that while they are suffering too, their sales are still better than others in the market.

“Despite the slowdown in India, Trump is still the most sought after luxury residential brand in the country,” Kalpesh Mehta, the developer of unfinished projects in Kolkata and Gurugram, said in a statement.