The matter has been referred to the DHS Inspector General for review.

Acting DHS Secretary Chad Wolf and acting DHS Deputy Secretary Ken Cuccinelli were named to their current roles in violation of the Vacancies Reform Act, according to a finding by the Government Accountability Office.

Wolf’s predecessor, former acting DHS Secretary Kevin McAleenan, was also performing in that role in violation of the act, according to the GAO. McAllenan was appointed to the role after DHS Secretary Kirstjen Nielson resigned in April of 2019.

In a blistering joint statement, House Homeland Security Committee Chairman Bennie Thompson and House Oversight and Reform Chairwoman Carolyn Maloney said Wolf should step down immediately and called Cuccinelli “woefully unqualified,” saying he should “immediately resign from the Federal government and retire his unprofessional official Twitter account.” They also called on the president to appoint a career official to run the department in lieu of a Senate-confirmed appointee.

“GAO’s damning opinion paints a disturbing picture of the Trump Administration playing fast and loose by bypassing the Senate confirmation process to install ideologues. In its haste to circumvent Congress’s constitutional role in confirming the government’s top officials to deliver on the President’s radical agenda, the Administration violated the Department’s order of succession, as required by law,” the statement said.

President Donald Trump has frequently praised Wolf’s performance, saying he has done a “fantastic job” as acting secretary, in particular for his role in the controversial federal response to violent demonstrations in Portland, Oregon. He has praised Cuccinelli as well, calling him “fantastic.”

The GAO finding has no legal force, but the matter has been referred to the DHS Inspector General for review.

McAleenan, who was serving as Director of U.S. Customs and Border Protection, was improperly appointed as acting secretary by Nielsen, according to the finding. Because there was not a Senate-confirmed deputy secretary at the time of Nielsen’s resignation, the appropriate official that should have taken the reins of the department was the director the Cybersecurity and Infrastructure Security Agency (CISA), the GAO found.

Wolf was previously confirmed as under secretary for strategy, policy, and plans, but because McAleenan improperly held the position of acting secretary, his designation allowing Wolf and Cuccinelli to take their current acting roles was also improper.

A DHS spokesman said in a statement, “We wholeheartedly disagree with the GAO’s baseless report and plan to issue a formal response to this shortly.”

Cuccinelli’s position in the Trump administration was in legal jeopardy even before he assumed the No. 2 job at Homeland Security.

The legitimacy of his prior role as acting director of U.S. Citizenship and Immigration Services (the sub-agency of DHS that handles legal immigration) was challenged by a group of asylum seekers and advocates in September 2019.

A U.S. District Judge Randolph Moss ruled in March that Cuccinelli “was not lawfully appointed to serve as acting Director” of USIS.

Thursday night, the government dropped its appeal in the case. The decision is expected to further expose the agency to legal challenges of the hard-line immigration measures enacted under Cuccinelli’s tenure.

“It’s been clear from the start: Ken Cuccinelli was unlawfully appointed to lead USCIS,” said Anne Harkavy of Democracy Forward, one of the advocacy groups that brought the challenge. “Today, the Trump administration retreated from its legal fight because it knows the law is not on its side. This is a victory for the rule of law and for the asylum seekers and immigrants hurt by the administration’s harmful policies.”

Two measures that limited the ability for asylum seekers to consult their lawyers and request continuances on cases were invalidated by a lower court in March. At the time, the court concluded that Cuccinelli’s appointment as USCIS director in June 2019 was unlawful.

The decision from the government to drop the case on Thursday marked a victory for families who were detained at two ICE detention centers in Texas where the asylum measures were first implemented.

Critics also allege DHS tactical teams from U.S. Customs and Border Protection, a DHS agency, detained protestors in Portland without probable cause. The U.S. Attorney for Oregon has referred the matter to the DHS Inspector General for investigation.

“The determination by an independent congressional watchdog today invalidates actions Mr. Cuccinelli and Mr. Wolf have taken and both should immediately step down from their illegal roles,” Senate Democratic Leader Chuck Schumer said in a statement.

ABC News’ Quinn Owen contributed to this report.