Sen. Richard Burr (R-N.C.) is chairman of the committee.
"Apparently the Republican chair of the Senate Intel Committee didn't get the memo from the majority leader that this case was closed", Sen.
He was also quizzed about direct communications he had with Julian Assange, the founder of WikiLeaks, which leaked damaging documents and communications stolen by Russians from Clinton's campaign.
Trump, who has blasted the investigations into him and Russian Federation, defended his son, who runs the Trump Organization - a private business that the Republican president still owns.
The subpoena for Trump Jr.'s testimony marks an escalation of the Senate Intelligence Committee's probe into Russian election interference.
Blumenthal was asked about what would happen if Trump Jr. didn't comply with the subpoena.
Trump called his son a "very good person", adding that the "last thing he needs is Washington DC".
Chief of staff Mick Mulvaney said Thursday he was not given a heads-up. Burr and the top Democrat on the committee, Virginia Sen. Trump Jr., the president said, had already testified for a "massive" amount of time.
The panel's investigation, led by Burr, has been running for more than two years, and the committee has interviewed numerous same witnesses who spoke to special counsel Robert Mueller's team.
McConnell's speech noted the importance of the committee's "upcoming report".
The sources said the senators want to question Trump Jr. about testimony he gave to the Senate Judiciary Committee in September 2017 which was subsequently contradicted by Michael Cohen, Trump's former lawyer who started his prison sentence this week in part for lying to Congress.
When asked if Trump Jr. told his father about the meeting, he told senators, "I did not".
"The Mueller report came out - that's the Bible - the Mueller report came out, and they said he did nothing wrong", he said.