Throughout his presidency, Donald Trump has proved himself adept at evading the controversies that have dogged him on a near-daily basis. With the vast powers of the presidency at his disposal, he often succeeds in pivoting the national conversation to focus on political terrain he finds more favorable, like immigration or crime.

But for weeks now, there has been one controversy the president has been unable to evade: the public clamor over his ties to Jeffrey Epstein, the deceased sex offender.

Now, with the release this week of new information from Mr. Epstein’s estate, including a suggestive note apparently signed by Mr. Trump, the drip-drip-drip of revelations is complicating the White House strategy of brushing off the entire controversy.

The president’s press secretary, Karoline Leavitt, on Tuesday was once again confronted with questions about the so-called Epstein files, a collection of documents from the law enforcement investigation into Mr. Epstein’s abuse of girls and women.

The White House has denied for weeks that Mr. Trump sent a bawdy birthday note to Mr. Epstein in 2003, the subject of an earlier Wall Street Journal report. But on Monday, the House Oversight Committee obtained the document and released it.