The administration said that Mr. Trump was hosting Mr. Abe and his wife as a “gift” to the Japanese leader and has said that any profits earned from the stays of members of foreign governments at Trump properties during his presidency would be donated to the United States Treasury, to avoid the appearance that he was cashing in on his office.

It may be a frequent arrangement. Mr. Trump, his aides say, believes in getting to know foreign leaders with whom he will be spending time and taking their measure in informal settings outside Washington.

“President Trump is a deal maker, and his coin of the realm is personal relationships and trying to convince people to negotiate a certain way in his favor, so this is what he does,” Kathryn Dunn Tenpas, a scholar at the Brookings Institution who has studied presidential travel, said.

Mr. Trump is not the first president to make use of a personal retreat to engage in informal diplomacy. George W. Bush hosted foreign leaders at his ranch in Crawford, Texas, while Bill Clinton used Camp David, the official presidential retreat near Thurmont, Md., as an informal backdrop for high-stakes diplomacy, including efforts to forge peace in the Middle East. But for Mr. Trump, his retreat is also a for-profit club that benefits his family business, from which he has declined to divest.

“It’s just one more example of using public office for private gain,” Richard W. Painter, a White House counsel to Mr. Bush who is an expert on government ethics, said. “He’s going to Trump this, Trump that — it’s clearly designed to raise the value of the brand and send the message to foreign leaders that you ought to patronize Trump properties if you want to get in good with the president.”

On Saturday, Mr. Trump appeared to have taken some steps to separate the personal from the political. While Mr. Trump and Mr. Abe shuttled from resort to resort in the armored presidential limousine known as the Beast, the flags that normally flutter on the front and the presidential seals that usually adorn the doors were absent, an indication that these were not official stops.