WASHINGTON — The Senate Intelligence Committee has subpoenaed Donald Trump Jr., the president’s eldest son, who met with Russians in June 2016 after being promised political dirt about Hillary Clinton, according to people familiar with the committee’s decision.

The younger Mr. Trump is the first of President Trump’s children to be subpoenaed in the continuing congressional investigations into Russia’s 2016 election interference, and the move by the Republican-led committee is a sign that some members of the president’s party are not aligned with his desire for a swift end to all of the Russia inquiries.

News of the subpoena came a day after Senator Mitch McConnell, Republican of Kentucky and the majority leader, sought to lower the curtain on the drama in Congress surrounding Russia’s efforts to sabotage the 2016 election. The end of the Mueller investigation, he said, meant “case closed.”

But the subpoena of the younger Mr. Trump shows that the Intelligence Committee, which is under Mr. McConnell’s jurisdiction, is proceeding with its vigorous investigation that — for the most part — has not degenerated into a partisan morass like a parallel investigation by the House.