WASHINGTON — The White House confirmed on Tuesday that President Trump was involved in drafting a misleading statement issued by his son about a meeting with a Russian lawyer last year, contradicting the president’s lawyer who repeatedly denied that Mr. Trump had anything to do with the statement.

The statement was drafted while the president was on Air Force One flying back from a summit meeting in Europe. It was issued in response to an impending news report that Donald Trump Jr., his eldest son, had met with a Russian lawyer with ties to the Kremlin during last year’s presidential campaign. That meeting has become the focus of investigators looking at contacts between Russia and associates of Mr. Trump.

The statement sent to The New York Times on July 8 said the meeting was primarily “about the adoption of Russian children” that had been ended by the Moscow government in retaliation for sanctions imposed by the United States. But the statement made no mention of the fact that the meeting was set up by an intermediary promising incriminating information about Hillary Clinton as “part of Russia and its government’s support for Mr. Trump,” as an email to his son put it.

Only after The Times reported that the meeting was set up with the stated purpose of passing along damaging material about Mrs. Clinton did the younger Mr. Trump confirm the reason. And only after The Times told his representatives that it had obtained the emails setting up the meeting and planned to publish them did the younger Mr. Trump release them himself.