The acting director of national intelligence, Joseph Maguire, did not meet the deadline set by the House Intelligence Committee to turn over materials that the committee chairman subpoenaed on Friday — the substance of a whistleblower complaint and relevant correspondence with the White House.

Chairman Adam Schiff said Tuesday he now expects Maguire to appear in open session this Thursday, "under subpoena if necessary." Schiff believes Maguire is withholding the whistleblower complaint in order to protect an even higher-ranking official, possibly a top administration official or even President Trump.

However, it is unclear how a second subpoena would be more enforceable than the first.

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In a letter with the first subpoena, Schiff alleged Maguire was unlawfully withholding the whistleblower complaint from the committee by "improperly" citing the complaint's "confidential and potentially privileged communications" as its reason for withholding it. While Schiff said he couldn't divulge the contents of the complaint, DNI's citing of "privileged communications" means it would involve a "pretty narrow group of people."

FILE: Nominee for director of the National Counterterrorism Center, Joseph Maguire, looks on during his confirmation hearing before the Senate Intelligence Committee on Capitol Hill in Washington, DC, on July 25, 2018. Marcus Tappan / AFP/Getty Images

The complaint was originally sent by someone in the Intelligence Community to its inspector general (ICIG), who found the whistleblower complaint was both credible and of "urgent concern," Schiff said. And that is why Schiff has said the Committee must move quickly.

Maguire does not agree. He wrote to Schiff Tuesday and disagreed with his characterization of the complaint.

"The complaint forwarded to the ICIG does not meet the definition of "urgent concern," Jason Klitenic, Office of the Director of National Intelligence, counsel wrote to Schiff. "This complaint ... concerned conduct by someone outside the Intelligence Community and did not relate to any 'intelligence activity' under the DNI's supervision ... the law did not require that the DNI forward the complaint to the Intelligence Committees."

Klitenic also assured Schiff in his letter that the whistleblower would "not be subject to retaliation or adverse consequences" as a result of having filed a complaint with the ICIG.

Schiff said in a statement Tuesday that the acting DNI "will be required to come before the Committee to tell the public why he is not following the clear letter of the law, including whether the White House or the Attorney General are directing him" to withhold the whistleblower complaint from the committee.

That is also not going to happen, Klitenic informed Schiff.

"Given the pressing responsibilities to which the DNI is devoted this week, he is not available on such short notice," Klitenic's letter reads. "We also believe that a hearing would not be a productive exercise while the ODNI remains engaged in deliberations over the appropriate response."

At this point, neither the acting DNI nor Schiff has said anything more to reveal about the nature of the complaint or who the subject of the complaint is. But Schiff has some ideas. "I think it's fair to assume this involves either the president or people around him or both," Schiff told CBS News' "Face the Nation" Sunday.

Reporting by Olivia Gazis.