What connects the two issues? Leverage.

It might not seem obvious what sanctions have to do with American parents’ adoptions of Russian children, which is the topic that the younger Mr. Trump initially said Ms. Veselnitskaya wanted to discuss. Their connection comes down to one word: leverage.

The context is the Magnitsky Act, a 2012 American law that freezes the assets held in the United States by Russian officials responsible for human rights abuses. The law also bars these officials from receiving American visas. It was named after Sergei Magnitsky, a young Russian lawyer who died in pretrial detention after exposing a $230 million tax-theft scam perpetrated by Russian officials.

To the law’s backers, the Magnitsky Act was a way to strike a blow for justice. But to Mr. Putin, it seemed like an intolerable attack by the United States government against the stability of his own presidency.

Mr. Putin, though powerful, depends on the support of a small circle of powerful elites, in and out of government, who both keep him in power and help him enforce his will. In exchange, Mr. Putin sees that they are taken care of. The Magnitsky Act, by sanctioning some of those elites, sent a message that Mr. Putin might not be able to uphold his end of the bargain.

It also called into question whether lower-ranked officials could trust that they would be protected from punishment for tolerating or participating in illegal acts at the behest of Mr. Putin or his allies.