Senate Judiciary Committee Chairman Lindsey Graham said Thursday that a vote to authorize subpoenas for documents and testimony from top Obama officials will take place in early June as part of his panel's investigation into the origins of the FBI’s Russia probe during the 2016 presidential election.

The committee on Thursday had a short meeting, where Graham referenced the potential subpoenas, which will be voted for approval on June 4. The potential subpoenas would cover documents, communications and witness testimony in a public setting or behind closed doors for any “current or former executive branch official or employee involved in the 'Crossfire Hurricane' investigation."

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Under committee rules, Graham cannot unilaterally issue a subpoena. The committee chairman can only issue a subpoena with the consent of the ranking member, Sen. Dianne Feinstein, D-Calif., or by a committee vote, which is slated to take place on June 4.

If approved by a majority of the committee on June 4, the subpoena authorization gives Graham the ability to issue a subpoena for witnesses, documents and/or other materials.

Graham is seeking testimony from former FBI Director James Comey, former FBI Deputy Director Andrew McCabe, former Director of National Intelligence James Clapper, former CIA Director John Brennan, former Deputy Attorney General Sally Yates and others.

The subpoena authorizations would also cover any documents, communications and testimony “related to any aforementioned matter” from current and former officials, including Trisha Anderson, James Baker, Dana Boenta, Mary McCord, Andrew McCabe, Loretta Lynch, Jonathan Moffa, Bruce Ohr, Lisa Page, Peter Strzok, Joseph Pientka, John Podesta, Samantha Power, Susan Rice, Rod Rosenstein, Bill Priestap, and Sally Yates among others.

The authorizations would also cover individuals involved in the Steele Dossier, including Fusion GPS founder Glenn Simpson and Nellie Ohr.

Graham announced last week that his investigation would specifically focus on unmasking, abuses of the Foreign Intelligence Surveillance Act, and the appointment of Robert Mueller as special counsel in May 2017.

Graham said that his panel will “begin holding multiple, in-depth congressional hearings regarding all things related to Crossfire Hurricane starting in early June.”

GRAHAM REQUESTS NAMES OF OFFICIALS WHO SOUGHT TO 'UNMASK' TRUMP CAMPAIGN, TRANSITION OFFICIALS

Crossfire Hurricane was the FBI’s internal code name for the investigation into whether members of the Trump campaign were coordinating with Russia during the 2016 presidential election. Mueller's team eventually announced that it found no evidence of coordination.

The first phase of the panel’s investigation “will deal with the government’s decision to dismiss” the case against former national security adviser Michael Flynn, as well as “an in-depth analysis of the unmasking requests made by Obama Administration officials against Gen. Flynn.”

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.

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

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As part of the committee's focus on unmasking, Graham on Tuesday wrote to Attorney General William Barr and acting Director of National Intelligence Richard Grenell requesting the names of Obama-era officials who sought to "unmask" the identity of members of the Trump campaign and Trump transition team in 2016.

“Given the extensive number of requests for the unmasking of General Flynn’s name during this short time period, it raises the question of whether these or other officials sought the unmasking of the identities of other individuals associated with the Trump campaign or transition team,” Graham wrote in the letter to Barr and Grenell.

The letter requests those who sought to unmask Trump officials, including President Trump and his children, as well as officials including Jared Kushner, Corey Lewandowski, Kellyanne Conway, Paul Manafort, Steve Bannon, Sam Clovis, Chris Christie, Carter Page and George Papadopoulos.

Graham's request comes after Grenell declassifed a list of Obama officials who sought to unmask Flynn during the presidential transition period. Requests came from Comey, Brennan, Clapper, then-U.N. Ambassador Samantha Power, and then-Vice President Joe Biden, among others.

Fox News' Adam Shaw contributed to this report.