The resort projects, which a Trump spokeswoman said this past week were “binding contracts,” have created a gray area of conflicting interests that could be hard to separate from an array of issues facing the United States and Indonesia, including trade and contested claims over the South China Sea.
Mr. Trump’s local partner on the resorts, Hary Tanoesoedibjo, is a billionaire media mogul with his own political ambitions. He ran for vice president of Indonesia in 2014 and is organizing a political party for another possible run at national office in 2019. If Mr. Hary or his party wins a major role in government, the potential conflicts could escalate significantly.
“You could have two world leaders that are business partners,” said Richard W. Painter, who served as a White House ethics lawyer during the George W. Bush administration. “It makes it almost impossible to conduct diplomacy in an evenhanded manner. That does not work.”
Through the partnership with Mr. Hary, Mr. Trump has gained access to some of Indonesia’s top political figures, including Setya Novanto, the speaker of the House of Representatives, who was temporarily forced to surrender his leadership post because of corruption allegations in 2015. Mr. Setya was heard on an audio recording seeking a $4 billion payment from the American mining giant Freeport-McMoRan.
Months before the recording came out in December 2015, Mr. Trump met with Mr. Setya during the presidential campaign at Trump Tower. After their lunch, Mr. Trump pulled Mr. Setya before the cameras at a news conference and called him “a great man,” adding, “We will do great things for the United States.”
The knot of potential conflicts includes Mr. Icahn, the billionaire investor who will serve as a special adviser to Mr. Trump. He is one of the largest shareholders in Freeport, which does so much business in Indonesia that it is the country’s largest taxpayer and has been seeking to extend its mining contract with the Indonesian government.
“This stuff is so murky,” said Karen Hobert Flynn, president of Common Cause, a nonprofit group that has called for Mr. Trump to sell off his businesses to avert conflicts of interest. “It is not going to be clean moving forward. There are going to be complications as these projects move forward.”
So far, Mr. Trump has provided little clarity about what he means by “no new deals,” a vow made in a Twitter post he sent out in mid-December. His aides suggested in a series of interviews during the past week that even if construction had not started on a project, the Trump Organization would move ahead if it had a binding agreement.
For Mr. Trump, the Indonesian deals are licensing and management agreements in which he provides the use of his name and his company manages the resorts.
Even though no structures were built, Mr. Trump secured a considerable payout on the two deals, according to a financial disclosure report that listed payments ranging from $1 million to $5 million for each of the projects between January 2015 through last May. That is far more than the $400,000 salary paid to the president, which Mr. Trump has said he will decline.
Mr. Trump created the corporations that manage these projects — including DT Bali Hotel Manager and DT Lido Hotel Manager — in late June 2015, just a week after he declared his intention to run for president.
His companies already have operations in at least 20 countries, including the Philippines, India, Turkey and Britain, but the full extent of his foreign financial ties is unclear because he has refused to release his tax returns or disclose the identity of his lenders.
In addition to the no-new-deals pledge, Mr. Trump has said that his sons, Eric and Donald Jr., along with other executives, will manage the family’s global real estate business.
The Trump Organization has recently moved to resolve potential controversies, in part by closing family foundations. It has also dropped a number of its proposed projects, including Trump Office Buenos Aires in Argentina; Trump Towers Rio and Trump Hotel Rio de Janeiro, both in Brazil; Trump International Hotel & Tower Baku in Azerbaijan; Trump Tower Batumi in Georgia; and Trump Riverwalk in Pune, India, representatives from the Trump Organization have said in the past week, in response to questions from The New York Times.
But other projects — including some on which construction has not started or is not well underway — are moving ahead, including Trump Tower Mumbai and a Trump tower in Gurgaon, both in India; Trump Tower Punta del Este in Uruguay; Trump International Golf Club, Dubai, and Trump World Golf Club, Dubai, both in the United Arab Emirates; and Trump International Hotel & Tower Vancouver, in Canada, the Trump Organization confirmed.
Amanda Miller, the Trump Organization spokeswoman, said of the two Indonesian projects, “Construction is well underway and will proceed as planned.”
In fact, construction has started only on a golf course and toll road as part of the Lido Lakes resort in West Java. Separating the enterprise from politics may also be difficult because Mr. Hary’s MNC Group is building the road to the site as part of a government highway project.
No new structures have been built at Lido Lakes or at the resort near the stunning Tanah Lot temple in Bali. A 20-year-old hotel, the Pan Pacific Nirwana Bali Resort, stands on the Bali property and could be renovated to create a Trump hotel, but that work has not begun.
In a recent interview in his Jakarta office, where an autographed Make America Great Again cap sits prominently on a table, Mr. Hary said he believed that his agreements with Mr. Trump did not present a conflict of interest for the president-elect.
“His family and children have the freedom to do business as long as it is arm’s length and unrelated to the president’s position,” he said.
The two resorts will give the Trump brand a high profile in Indonesia — which has the world’s largest Muslim population — with the Trump name adorning two luxury hotels and premier golf courses as well as high-end villas and condominiums. Yet the American president’s name on the projects could also make them potential targets. During the campaign, Mr. Trump made statements about Muslims widely viewed as inflammatory. American hotels in Jakarta have been attacked by terrorists several times.
Mr. Hary said he began the partnership with Mr. Trump in 2015 when he was looking for a hotel partner for the resorts, but said he had negotiated a deal with his children before ever meeting with Mr. Trump.
“It’s the children who run the company,” he said.
After signing one deal and negotiating the other, he helped arrange a meeting in New York in September 2015 between Mr. Trump and his good friend, Mr. Setya, the House speaker, and Fadli Zon, the deputy speaker, whose district includes the city of Bogor, where the Lido project is.
Mr. Trump met the two politicians and several others for lunch at Trump Tower, where, among other things, they discussed the resort projects, the participants said.
“He was very warm, very enthusiastic,” Mr. Fadli said. “He likes Indonesia. He knows about his investment in Indonesia, in Bali and Bogor. And he likes Indonesia, a big democratic Muslim country.”
After lunch, Mr. Trump invited the Indonesians to join him downstairs for a campaign news conference, they said. When the event was ending, Mr. Trump brought Mr. Setya to the lectern and introduced him to the crowd, calling him “one of the most powerful men, and a great man.”
Mr. Trump then turned to Mr. Setya. “Do they like me in Indonesia?” he asked.
Mr. Setya smiled and replied “yes.”
The event drew criticism in Indonesia, where some accused the Indonesian politicians of meddling in a foreign election. But Mr. Setya and Mr. Fadli said they had been invited to the news conference and it would have been impolite to refuse.
“Nowadays, after Trump became president-elect, people came to appreciate what I did,” Mr. Setya told The Times in a recent interview.
Mr. Setya, who heads Parliament’s second-largest party, said he had requested another meeting with Mr. Trump before his inauguration to discuss a possible business deal, although he declined to say what it was. He said he also would carry a message to Mr. Trump from the Indonesian president, Joko Widodo.
Soon after returning from the New York meeting with Mr. Trump in 2015, Mr. Setya became embroiled in scandal. He was heard on the audio recording asking for 20 percent of the shares of Freeport’s Indonesian subsidiary in exchange for helping the company extend its operating contract with the government. The value of the shares was about $4 billion.
The episode exploded into a Watergate-style moment, with the local news media repeatedly playing the damning portions of the recording to a rapt public. Mr. Setya defended the demand as a joke.
Mr. Setya was recently reinstated as speaker after a court ruled the recording was inadmissible as evidence.
Mr. Fadli said he could see a role for President Trump in resolving the thorny Freeport issue. “Definitely he has to be involved in that because it is a big investment,” he said.
Mr. Painter, the former White House ethics lawyer, said these complications demonstrated why Mr. Trump’s company should not be involved in foreign property deals like those in Indonesia.
“They should be trying to pull out of deals around the world like this, rather than trying to expand,” he said.
On Wednesday, Mr. Trump accused the news media of exaggerating any potential conflicts presented by his business holdings.
“It’s not a big deal; you people are making it a big deal, the business,” Mr. Trump said on the steps of his Mar-a-Lago resort in Florida, where he was spending the holidays. “They all knew I had big business all over the place.”