Representatives for both men did not immediately respond to requests for comment.

Ms. Veselnitskaya arrived the next day and was ushered into Donald Trump Jr.’s office for a meeting with what amounted to the Trump campaign’s brain trust.

Besides having politically connected clients, one of whom was under investigation by federal prosecutors at the time of the meeting, Ms. Veselnitskaya is well known for her lobbying efforts against the Magnitsky Act, a 2012 law that punishes designated Russian human rights abusers by allowing the United States to seize their assets and keep them from entering the country. The law so angered Mr. Putin that he retaliated by barring American families from adopting Russian children. Her activities and associations have brought her to the attention of the F.B.I., according to a former senior law enforcement official.

When first contacted by The Times on Saturday, Donald Trump Jr. portrayed the meeting this way: “It was a short introductory meeting. I asked Jared and Paul to stop by. We primarily discussed a program about the adoption of Russian children that was active and popular with American families years ago and was since ended by the Russian government, but it was not a campaign issue at the time and there was no follow-up.”

Responding to Queries

The next day, after The Times informed him that it was preparing an article that would say that the meeting also involved a discussion about potentially compromising material on Mrs. Clinton, he issued another statement: “I was asked to have a meeting by an acquaintance I knew from the 2013 Miss Universe pageant with an individual who I was told might have information helpful to the campaign. I was not told her name prior to the meeting. I asked Jared and Paul to attend, but told them nothing of the substance.”

He continued: “After pleasantries were exchanged, the woman stated that she had information that individuals connected to Russia were funding the Democratic National Committee and supporting Ms. Clinton. Her statements were vague, ambiguous and made no sense. No details or supporting information was provided or even offered. It quickly became clear that she had no meaningful information. She then changed subjects and began discussing the adoption of Russian children and mentioned the Magnitsky Act. It became clear to me that this was the true agenda all along and that the claims of potentially helpful information were a pretext for the meeting.”

Mr. Goldstone recalled the meeting in much the same way.

Ms. Veselnitskaya offered “just a vague, generic statement about the campaign’s funding and how people, including Russian people, living all over the world donate when they shouldn’t donate” before turning to her anti-Magnitsky Act arguments, he said. “It was the most inane nonsense I’ve ever heard.”

Ms. Veselnitskaya, for her part, said in an statement to The Times sent this past weekend that “nothing at all about the presidential campaign” had been discussed at the Trump Tower meeting, adding that she had “never acted on behalf of the Russian government” and that she had “never discussed any of these matters with any representative of the Russian government.” She has not responded to requests for comment since.