WASHINGTON — Donald Trump Jr. has agreed to testify next month before the Republican-led Senate Intelligence Committee, a source close to the president's eldest son confirmed to NBC News on Tuesday.

The source said that the closed-door session will be under oath and is expected to take place in mid-June. It will be limited to five to six topics and Trump Jr.'s appearance will last between two and four hours.

This comes after the Intelligence Committee, chaired by Sen. Richard Burr, R-N.C., said last week that it had issued a subpoena for Trump Jr. to answer questions about his assertion that he only had limited knowledge of a project to build a Trump Tower in Moscow.

The scope and length of the testimony were the major sticking points between Trump Jr. and the committee, the source said, adding that the president's son was was prepared to defy the subpoena until late Monday afternoon when the panel reached out to Trump Jr.s legal team to discuss an agreement.

President Donald Trump said last week that he was surprised his son was subpoenaed.

"My son is a very good person, he works very hard," Trump said. "The last thing he needs is Washington, D.C."

Burr received significant blowback from Republicans for issuing the subpoena after Senate Majority Leader Mitch McConnell, R-Ky., declared last week that it was "case closed" on the Russia investigation in the wake of the release of special counsel Robert Mueller report.

Meanwhile, the Democratic-led House Intelligence Committee is investigating whether personal lawyers for Trump and his family tried to obstruct special counsel Robert Mueller's investigation by helping Michael Cohen deliver false testimony.

The committee's chairman, Rep. Adam Schiff, D-Calif., sent letters to four lawyers requesting documents related to Cohen, who told Congress in public testimony in February that the attorneys helped edit inaccurate testimony from 2017 that Cohen gave to lawmakers about a Trump Tower project in Moscow.

"Among other things, it appears that your clients may have reviewed, shaped and edited the false statement that Cohen submitted to the committee, including causing the omission of material facts," Schiff said in one of the letters obtained by NBC News on Tuesday. The story was first reported by The New York Times.

In his opening statement to Congress earlier this year, Cohen, who recently started a three-year prison sentence, said that Trump lied about his ongoing efforts to build a Trump Tower in Moscow during the 2016 campaign election and the president had suggested Cohen lie.

The attorneys are Trump's lawyer, Jay Sekulow, Donald Trump Jr.'s lawyer, Alan S. Futerfas, Trump Organization lawyer Alan Garten and Ivanka Trump's lawyer, Abbe D. Lowell.

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A May 3 letter from Schiff to the lawyers' representatives asked that the attorneys "produce the requested documents and contact the committee staff to schedule dates for voluntary interviews" no later than last Thursday.

"Material in the Committee's possession, as well as Michael Cohen's Committee testimony and admissions to the Special Counsel's Office, raise serious, unresolved concerns about the obstruction of our Committee's investigation that we would be negligent not to pursue," Schiff said in the statement.

"If any individual is allowed to lie to our committee or encourage others to do so, hide behind inapplicable privileges, or otherwise fail to provide anything less than full cooperation, other witnesses will be emboldened to similarly obstruct, both now and in the future. We must not allow that to happen," he added.

Patrick Strawbridge, who is Sekelow's lawyer, released a statement Tuesday on behalf of the four lawyers.

"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," he said. "As committed defense lawyers, we will respect the constitution and defend the attorney-client privilege — one of the oldest and most sacred privileges in the law."