WASHINGTON—President Donald Trump’s eldest son on Wednesday refused to discuss with congressional investigators a father-son conversation earlier this year about how to handle fallout from revelations that he met with a Russian attorney during the 2016 campaign, according to people familiar with the matter.

During the more than seven-hour session with the House Intelligence Committee, Donald Trump Jr. invoked attorney-client privilege when asked for details about a telephone conversation he had with his father after news broke about his meeting with Russian attorney Natalia Veselnitskaya, the people familiar with the matter said. The younger Mr. Trump has publicly said he met with the attorney to obtain negative information on Democratic nominee Hillary Clinton.

Attorneys for both the president and his son were on the call, which took place sometime after a July 8, 2017 New York Times story about the meeting, according to the people familiar with the matter.

An attorney for the younger Mr. Trump didn’t immediately respond to a request for comment. A White House lawyer declined to comment.

The House committee, as well as Senate investigators and Special Counsel Robert Mueller, are separately investigating Russia’s activities during the campaign and whether the Trump campaign colluded with Moscow. Russia has denied interfering in the campaign, and the president has said his team did nothing wrong.