Acting Homeland Security Secretary Chad Wolf speaks during a roundtable discussion on community safety, at Mary D. Bradford High School in in Kenosha, Wisconsin on September 1, 2020. (Photo by MANDEL NGAN / AFP) (Photo by MANDEL NGAN/AFP via Getty Images)
CNN  — 

The Department of Homeland Security inspector general declined to investigate whether acting Homeland Security Secretary Chad Wolf and his deputy Ken Cuccinelli are serving in their roles lawfully, saying its efforts on the issue would be “pointless.”

DHS Inspector General Joseph Cuffari cited “troubling aspects” with an August Government Accountability Office report that found that the two senior officials were appointed as part of an invalid order of succession.

In its report, the GAO referred the legality of actions taken by Wolf and Cuccinelli, as well as the question over who should be serving in the top two roles, to the DHS inspector general.

The inspector general’s decision comes after a federal judge in Maryland ruled that Wolf is likely unlawfully serving as acting secretary and leaves the issue of leadership at the department at an impasse. In March, a different federal judge ruled that it was unlawful to appoint Cuccinelli, an immigration hardliner, to lead the agency responsible for processing US immigration requests.

However, both Wolf and Cuccinelli remain in their positions. Cuccinelli currently fills two leadership roles at DHS – the senior official performing the duties of the deputy secretary and the director of US Citizenship and Immigration Services.

Cuffari concluded that under the circumstances “it would be pointless” for the inspector general “to add its voice to what has become a bitter inter-branch disagreement.”

“Neither GAO nor DHS OIG can issue a binding determination on that issue, but a federal court can and probably will,” Cuffari wrote in response to Democratic Reps. Bennie Thompson of Mississippi and Carolyn Maloney of New York.

The lawmakers requested the investigation last November and want both men to resign. In late August, the GAO reaffirmed its initial findings, after the department requested the report be rescinded.

This is the first communication from the DHS inspector general’s office on the topic that the GAO has seen, according to GAO spokesperson Chuck Young. “We are confident in our thorough and well documented initial legal determinations. A federal judge in Maryland cited our decision favorably yesterday in a related matter,” Young said in a statement.

Homeland Security spokesperson Alexei Woltornist said in a statement Tuesday that “GAO’s report was erroneous, non-binding, and issued under highly questionable authority under federal law,” again urging the GAO to reconsider its report.

The inspector general’s office is investigating several recent complaints about the department, including allegations that DHS law enforcement personnel improperly detained and transported protestors, whether DHS’ Office of Intelligence and Analysis improperly gathered intelligence on US journalists, as well as an overall review of DHS’ deployment of law enforcement officers to Portland, Oregon.

CNN’s Priscilla Alvarez contributed to this story.