Cruz: Holder 'absolutely' should resign amid controversies

"Yes, absolutely," Cruz told Fox News when asked if Holder should go. "I think the reason is this Department of Justice has demonstrated a willingness to disregard the law."

Cruz, who worked in the department during the Bush administration, accused Holder's Justice Department of "not respecting the Bill of Rights" and using "the machinery of the federal government ... as a partisan tool to punish those perceived as your political enemies."

"It's unprecedented," Cruz said. "The degree of willingness of the administration to target a reporter for this network as an unindicted co-conspirator? That is unprecedented."

Holder reportedly signed off on a subpoena of Fox News Ccrrespondent James Rosen’s personal records that characterized the reporter as a co-conspirator with the government employee accused of leaking to him information about North Korea in violation of federal law. Rosen was not prosecuted, but media organizations have argued that the move sets a dangerous and chilling precedent.

The Justice Department has also come under fire for the subpoena of phone records belonging to Associated Press reporters and editors. Holder had planned to meet Thursday with representatives from top media organizations, although many indicated they would not participate if the conference was kept off-the-record.

Last week, President Obama announced Holder would launch a review into the Justice Department's targeting of journalists, with a report expected by July 12.

But that move has drawn criticism from Republicans, who argue Holder has essentially been tasked with leading an investigation into himself.

"The conduct of the Justice Department does not inspire confidence," Cruz said.

Asked Thursday about the president's confidence in Holder, White House spokesman Josh Earnest said Obama was "not in the least" worried about the attorney general's ability to do his job amid all the scrutiny.