Cohen's original incriminating statement involved the timing of the Trump Organization's negotiations with Russian Federation for a Trump Tower in Moscow.
Patrick Strawbridge, representing Sekulow, responded in a statement, "Instead of addressing important intelligence needs, the House Intelligence Committee appears to seek a truly needless dispute - this one with private attorneys - that would force them to violate privileges and ethical rules".
A committee spokesperson declined to comment.
The panel had subpoenaed Trump Jr.to appear before the committee, two congressional sources said last week.
In the wake of Robert Mueller's report, Democrats and a subset of Republicans have argued that the meeting, in which Trump Jr. and other campaign officials met with a Kremlin-linked attorney, warrants further investigation.
What's more, it further clears Trump, Jr. -who did nothing wrong with regard to Russian Federation, despite countless media and Democrat attacks on his character. Michael Cohen is a worthless witness, and if I were Donald Trump Jr.'s lawyer I would tell him, 'You don't need to go back into this environment anymore, you've been there for hours and hours and hours. Negotiations over another appearance dragged on and eventually stalled, leading to the subpoena compelling the president's son to testify or risk being held in contempt. "I don't know why. But it seems very unfair to me".
"None of us tell Chairman Burr how to run his committee", McConnell said.
Still, McConnell made it clear that he is eager to be finished with the probe, which has now gone on for more than two years.
"He's indicated publicly he believes they will find no collusion, and we are hoping that we will get a report on that subject sometime soon", McConnell said about Burr.
Three people familiar with Burr's remarks described them to The Associated Press. Trump Jr. previously told the Senate Judiciary Committee that he was "peripherally aware" of a Cohen-coordinated project in 2015-2016 to have a Trump Tower built in Moscow.
Speaking to reporters at the White House on Tuesday, President Trump called the Senate Intelligence Committee's move to subpoena his son "unfair".
Allies of President Trump have expressed irritation with Sen.