The head of the House Intelligence Committee is inviting special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE to testify before his panel sometime in May, claiming that the public must learn about the Russia probe's findings outside of what he sees as Attorney General William Barr Bill BarrHarris faces pivotal moment with Supreme Court battle Hillicon Valley: DOJ proposes tech liability shield reform to Congress | Treasury sanctions individuals, groups tied to Russian malign influence activities | House Republican introduces bill to set standards for self-driving cars McCarthy threatens motion to oust Pelosi if she moves forward with impeachment MORE's partisan takes.

Intelligence Chairman Adam Schiff Adam Bennett SchiffPelosi, Democrats unveil bills to rein in alleged White House abuses of power Chris Matthews ripped for complimenting Trump's 'true presidential behavior' on Ginsburg Trump casts doubt on Ginsburg statement, wonders if it was written by Schiff, Pelosi or Schumer MORE (D-Calif.) sent a letter on Thursday to Mueller stating that he will work with the special counsel "to secure a mutually agreeable date in May.”

The committee argued that it must be briefed about all the details of the counterintelligence probe — classified or not — as part of its duty to conduct oversight on matters of intelligence and counterintelligence.

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“To discharge its distinct constitutional and statutory responsibility, the Committee must be kept ‘fully and currently informed’ of the intelligence and counterintelligence findings, evidence, and implications for your investigation," Schiff wrote to Mueller.

"This requires that the Committee receive the comprehensive testimony from you about the investigation’s full scope and areas of inquiry, its findings and underlying evidence, all of the intelligence and counterintelligence information gathered in the course of the investigation, and the status of any ongoing counterintelligence investigation," he continued.

His letter comes shortly after House Judiciary Committee Chairman Jerrold Nadler Jerrold (Jerry) Lewis NadlerDemocrats shoot down talk of expanding Supreme Court Schumer: 'Nothing is off the table' if GOP moves forward with Ginsburg replacement Top Democrats call for DOJ watchdog to probe Barr over possible 2020 election influence MORE also called on Mueller to testify before his committee "as soon as possible," following the conclusion of Barr's press conference Thursday morning in which he laid out Mueller's findings and why certain redactions were made.

“As I have already communicated to the Department of Justice, I request your testimony before the Judiciary Committee as soon as possible — but, in any event, no later than May 23, 2019,” Nadler wrote to Mueller.

The two committees both claim to have a stake in examining the investigative findings, and thereby having Mueller testify. The Judiciary Committee has jurisdiction over the Justice Department and it would also be the committee to handle impeachment proceedings were those to get underway, while the Intelligence Committee has investigated Russia's interference in the 2016 election and has jurisdiction over counterintelligence matters.

The jockeying for Mueller's congressional appearance comes on the same day Barr released a redacted version of Mueller's report to Congress and the public. During his press conference, Barr said he has no objections to Mueller testifying before Congress.

Mueller's report says the investigative team "did not establish that members of the Trump Campaign conspired or coordinated with the Russian government" in its election interference efforts. But the special counsel also wrote that their evidence prevents "conclusively determining that no criminal conduct occurred" in terms of the obstruction of justice case.

While Mueller did not make a determination on the matter either way, Barr, along with Deputy Attorney General Rod Rosenstein Rod RosensteinDOJ kept investigators from completing probe of Trump ties to Russia: report Five takeaways from final Senate Intel Russia report FBI officials hid copies of Russia probe documents fearing Trump interference: book MORE and other DOJ counsels, determined that the evidence did not reach a threshold to charge President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE of obstruction.

Barr's involvement is a flashpoint for Democrats who say the attorney general has revealed he is a Trump loyalist who is seeking to protect the president, while also seeking to shape the narrative in favor of Trump.