Mr. Trump’s comments about Mr. Cohen on Saturday, made during a friendly interview with Jeanine Pirro of Fox News, were his first extended remarks on the matter since Mr. Cohen’s congressional testimony was announced. Asked by Ms. Pirro if he was “worried” about the testimony, Mr. Trump called Mr. Cohen “weak” and asserted — in contradiction to filings by federal prosecutors in Manhattan — that Mr. Cohen had “no information” on him.

“He’s in trouble on some loans and fraud and taxicabs and stuff that I know nothing about,” Mr. Trump said. “And in order to get his sentence reduced, he says, I have an idea, I’ll tell — I’ll give you some information on the president.”

Mr. Trump then implied that Mr. Cohen ought to be sharing information instead on his father-in-law, whose name he said he did not know.

“But he should give information maybe on his father-in-law, because that’s the one that people want to look at,” he said, adding, “That’s the money in the family.” Pressed by Ms. Pirro for more details, Mr. Trump said, “I don’t know, but you’ll find out, and you’ll look into it because nobody knows what’s going on over there.”

Mr. Cohen’s father-in-law, Fima Shusterman, emigrated from Ukraine in 1975. The year before his daughter’s marriage to Mr. Cohen, he pleaded guilty to evading federal reporting requirements for large cash transactions, admitting that he had cashed $5.5 million worth of checks to evade disclosure laws. He was sentenced to probation after cooperating with prosecutors in a related case.

Saturday was not the first time Mr. Trump has targeted Mr. Cohen’s family. After Mr. Cohen pleaded guilty to his crimes, the president said Mr. Cohen had done so only to save his wife and his father-in-law.

As they prepared to indict him, prosecutors had signaled to Mr. Cohen that his wife could be implicated, since she had also signed his tax returns. That threat helped push Mr. Cohen to plead guilty to the charges, according to a person familiar with the events.