Senate Judiciary Committee Chairman Lindsey Graham said Thursday that his panel would begin holding hearings as part of its investigation into the origins of the Trump-Russia probe, and would focus on unmasking, abuses of the Foreign Intelligence Surveillance Act, and the appointment of Robert Mueller as special counsel.

Graham, R-S.C., just hours after the president tweeted demanding that he call former President Barack Obama to testify before the committee, announced that his panel will “begin holding multiple, in-depth congressional hearings regarding all things related to Crossfire Hurricane starting in early June.”

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Crossfire Hurricane was the FBI’s internal code name for the investigation into whether members of the Trump campaign were coordinating or colluding with Russia during the 2016 presidential election.

Graham outlined what he called the “first phase” of the committee’s investigation, which he said “will deal with the government’s decision to dismiss the Flynn case as well as an in-depth analysis of the unmasking requests made by Obama administration officials against Gen. Flynn.”

“We must determine if these requests were legitimate,” Graham said.

Sens. Chuck Grassley, R-Iowa, and Ron Johnson, R-Wis., made public on Wednesday a list of Obama officials who purportedly requested to “unmask” the identity of Flynn, who at the time was Trump’s incoming national security adviser.

The list was declassified by Acting Director of National Intelligence Richard Grenell and sent to Grassley and Johnson.

The roster featured top-ranking figures including then-Vice President Joe Biden, then-FBI Director James Comey, then-CIA Director John Brennan, then-Director of National Intelligence James Clapper, and Obama’s then-chief of staff Denis McDonough.

As Fox News previously reported, Grenell had made the decision to declassify information about Obama administration officials who were involved in the “unmasking” of Flynn — whose calls with the former Russian ambassador during the presidential transition were picked up in surveillance and later leaked. His case has returned to the national spotlight after the DOJ moved to dismiss charges against him of lying to the FBI about those conversations, despite a guilty plea that he later sought to withdraw.

The declassified list, released Wednesday, specifically showed officials who “may have received Lt. Gen Flynn’s identity in response to a request processed between 8 Nov. 2016 and 31 Jan. 2017 to unmask an identity that had been generically referred to in an NSA foreign intelligence report,” the document said.

The document added: “While the principals are identified below, we cannot confirm they saw the unmasked information.”

Officials requesting such a name in this process do not necessarily know the identity in advance.

Meanwhile, Graham said the second area of inquiry for the committee would take place later this summer, and would be focused on Foreign Intelligence Surveillance Act abuses outlined by Justice Department Inspector General Michael Horowitz. Graham said that section of his investigation would focus on the FISA warrants obtained against former Trump campaign aide Carter Page.

“My goal is to find out why and how the system got so off the rails,” Graham said.

Graham added that the committee will also look at "whether Robert Mueller should have ever been appointed as special counsel.”

“Was there legitimate reason to conclude the Trump campaign had colluded with the Russians?” Graham questioned.

Graham first announced his investigation into the origins of the Trump-Russia probe after Mueller released his long-awaited report.

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A source told Fox News that the committee would invite the ex-officials to appear but would subpoena them if they encounter resistance. The source told Fox News that Senate investigators are looking at “various pieces” coming from “various sources” as part of their investigation.

Meanwhile, Graham did not appear keen to go along with Trump's call for him to have Obama appear before the committee.

“If I were a Senator or Congressman, the first person I would call to testify about the biggest political crime and scandal in the history of the USA, by FAR, is former President Obama,” Trump tweeted Thursday. “He knew EVERYTHING.”

“Do it @LindseyGrahamSC, just do it,” he continued. “No more Mr. Nice Guy. No more talk!”

A source familiar told Fox News that the president has been frustrated with Graham and the timeline of his committee's investigation. The source said Graham should have done interviews and the investigation should be further along by now.

But Graham raised serious concerns about the implications of calling the former president to testify.

“I am greatly concerned about the precedent that would be set by calling a former president for oversight. No president is above the law,” Graham said Thursday. “However, the presidency has executive privilege claims against other branches of government.”

“To say we are living in unusual times is an understatement. We have the sitting president (Trump) accusing the former president (Obama) of being part of a treasonous conspiracy to undermine his presidency,” Graham said. “We have the former president suggesting the current president is destroying the rule of law by dismissing the Gen. Flynn case.”

LIST OF OFFICIALS WHO SOUGHT TO 'UNMASK' FLYNN RELEASED: BIDEN, COMEY, OBAMA CHIEF OF STAFF AMONG THEM 

He added: “All of this is occurring during a major pandemic.”

Graham added that “both presidents are welcome to come before the committee and share their concerns about each other.”

“If nothing else it would make for great television,” he said. “However, I have great doubts about whether it would be wise for the country.”