Donald Trump Jr. has reached a deal to testify before the Senate Intelligence Committee sometime in mid-June, according to a source familiar with the matter. Trump Jr. was subpoenaed by the GOP-led committee last week to answer questions about his previous Russia-related testimony before the committee.

The source said Trump Jr. will testify before the committee for a limited amount of time — two to four hours — in mid-June. The New York Times first reported a deal had been reached for his testimony. As was the case in 2017, Trump Jr. will be questioned behind closed doors.

Allies of President Trump have expressed irritation with Sen. Richard Burr, the Republican chairman of the committee, for issuing a subpoena to the president's son as the GOP tries to move on from the report by special counsel Robert Mueller. Senate Majority Leader Mitch McConnell said the question of whether the Trump campaign conspired with Russia to affect the 2016 election was "case closed."

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Mueller's report detailed 10 possible instances of obstruction of justice and extensive Russian interference into the 2016 presidential election.

Trump Jr. was a key figure in the June 2016 meeting in Trump Tower with a Russian lawyer. And, according to former Trump attorney Michael Cohen, Trump Jr. was involved in discussions about the possibility of building a Trump Tower in Moscow.

Acting White House chief of staff Mick Mulvaney told CBS News' Major Garrett he was not told by the committee that the president's son would be subpoenaed. On "The Takeout" podcast, Mulvaney was critical of the GOP-led committee for not informing the White House.

For the Senate Intelligence Committee to subpoena Mr. Trump's son and "not at least get a heads-up, I thought was — let's say bad form," he said. He said he did not know whether the president was also caught by surprise.

Republicans have accused the investigation of being politically motivated. Sen. Lindsey Graham, a staunch supporter of Mr. Trump, told reporters Tuesday that if he were Trump Jr.'s lawyer, "I wouldn't put him back in this circus."

"Mueller to me is the final word on all things Trump and Russia. The family, I think, cooperated extensively, along with the Trump campaign," Graham said. "I admire Richard Burr. But here's what we've got to realize as oversight chairmen: there's criminal liability exposure to people who voluntarily submitted themselves to multiple investigations."

Senate Majority Leader Mitch McConnell has declined to speak out against the subpoena, saying on Tuesday, "none of us tell Chairman Burr how to run his committee."

"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.

A spokesperson for the committee told CBS News last week, "We do not discuss the details of witness engagements with the committee. Throughout the investigation, the committee has reserved the right to recall witnesses for additional testimony as needed, as every witness and witness counsel has been made aware."

Nancy Cordes contributed to this report.