“Obviously I’m the first person on a campaign to ever take a meeting to hear info about an opponent... went nowhere but had to listen,” he wrote in one tweet. In another, he added, “No inconsistency in statements, meeting ended up being primarily about adoptions. In response to further Q’s I simply provided more details.”

The younger Mr. Trump, who had a reputation during the campaign for having meetings with a wide range of people eager to speak to him, did not join his father’s administration. He runs the family business, the Trump Organization, with his brother Eric.

On Monday, after news reports that he had hired a lawyer, he indicated in a tweet that he would be open to speaking to the Senate Intelligence Committee, one of the congressional panels investigating Russian meddling in the election. “Happy to work with the committee to pass on what I know,” the younger Mr. Trump wrote.

Mr. Goldstone represents the Russian pop star Emin Agalarov, whose father was President Trump’s business partner in bringing the Miss Universe pageant to Moscow in 2013. In an interview Monday, Mr. Goldstone said he was asked by Mr. Agalarov to set up the meeting with Donald Trump Jr. and the Russian lawyer, Natalia Veselnitskaya.

“He said, ‘I’m told she has information about illegal campaign contributions to the D.N.C.,’” Mr. Goldstone recalled, referring to the Democratic National Committee. He said he then emailed Donald Trump Jr., outlining what the lawyer purported to have.

But Mr. Goldstone, who wrote the email over a year ago, denied any knowledge of involvement by the Russian government in the matter, saying that never dawned on him. “Never, never ever,” he said. Later, after the email was described to The Times, efforts to reach him for further comment were unsuccessful.

In the interview, he said it was his understanding that Ms. Veselnitskaya was simply a “private citizen” for whom Mr. Agalarov wanted to do a favor. He also said he did not know whether Mr. Agalarov’s father, Aras Agalarov, a Moscow real estate tycoon known to be close to President Vladimir V. Putin of Russia, was involved. The elder Mr. Agalarov and the younger Mr. Trump worked together to bring a Trump Tower to Moscow, but the project never got off the ground.