Mr. Duhnke, a former senior Republican congressional aide, was appointed by the SEC in December 2017. His tenure was marked by turmoil at the agency, with staff departures and complaints that Mr. Duhnke created “a sense of fear,” according to a whistleblower complaint and people familiar with the situation.

It isn’t clear how the SEC could punish Mr. Duhnke—if an investigation found misconduct—since commissioners already dismissed him. The 2002 Sarbanes Oxley law, which created the PCAOB after the Enron Corp. accounting scandal, gives the SEC authority to censure board members or remove them from office if they shirk their duties or abuse their authority.

The SEC’s examinations arm is also looking into how the PCAOB has been run, including its handling of whistleblowers and other employees, the people familiar with the matter said. Mr. Duhnke allegedly retaliated against employees he disagreed with by forcing them out of their jobs and, in certain cases, making it hard for them to get other jobs in government, whistleblowers alleged. One letter, sent to the PCAOB’s board in May 2019, said it was written by a group of current and former PCAOB employees. They later sent it to the SEC.

Mr. Duhnke said in a written statement that “every single allegation of wrongdoing that has been made against me is false. It’s obvious that certain individuals have abused their positions of authority by orchestrating a well-coordinated smear campaign.” He has previously said he upset some employees by making long-overdue changes to the organization.

Gary Gensler,

the new SEC chair, said he ousted Mr. Duhnke because the watchdog isn’t adequately fulfilling its mission of auditing the auditors. The PCAOB has fallen short on setting audit standards, taking effective enforcement actions against accounting firms, and liaising with investors—most of its duties—Mr. Gensler told The Wall Street Journal CFO Network event this month.

A PCAOB spokeswoman declined to comment on Mr. Gensler’s remarks and on the investigation. An SEC spokesman said the agency wouldn’t comment, saying it doesn’t acknowledge the existence of enforcement investigations because they are confidential.

Whistleblowers have also alleged Mr. Duhnke took a political approach to his job, firing senior staff and curtailing areas of the regulator’s work with the aim of shutting it down. The Trump administration in 2020 proposed folding the PCAOB into the SEC.

Investor representatives complained to the SEC this year that the regulator was too close to the accounting industry and had lost sight of its investor-protection mission.

The SEC probe is the second major review of the PCAOB in two years. It follows a turbulent period for the regulator, including a scandal in which auditors working for accounting firm KPMG LLP cheated on its exams, shake-ups of its board, the abrupt exits of many senior staff and allegations of racial discrimination.

Mr. Gensler’s recent move to replace the entire five-member PCAOB’s board is the second time in four years that happened under a new administration.

The PCAOB has hired law firm Sullivan & Cromwell LLP to investigate the retaliation allegations and deal with the SEC’s enforcement investigation, people familiar with the inquiry said.

Separately, the regulator has also hired law firm Covington & Burling LLP to investigate allegations of racial discrimination against Mr. Duhnke by

Sue Lee,

a former PCAOB chief risk officer who was fired last year, according to people familiar with the matter. Ms. Lee filed a lawsuit against Mr. Duhnke and the PCAOB earlier this year claiming unlawful termination. She said he had made disparaging comments related to her Chinese ancestry and referred to the coronavirus as the “Kung Flu” in her presence.

Mr. Duhnke and the PCAOB have denied Ms. Lee’s allegations and countersued her, claiming she was fired for cause.

A spokeswoman for Covington & Burling didn’t respond to requests for comment.

The SEC investigation comes barely two years after the agency ordered an outside review of the watchdog. In 2019, the SEC appointed one of its former chairs,

Harvey Pitt,

to review how the PCAOB was run.

The SEC hasn’t released Mr. Pitt’s report. One of the people familiar with the matter said the report included a laundry list of recommendations. It found the board didn’t operate sufficiently openly and handled the whistleblowers’ claims poorly, the person said. But the report didn’t conclude that Mr. Duhnke was politically motivated in trying to shake up the audit watchdog, the person added.

Before Mr. Gensler took over, the acting SEC chair ordered SEC officials to look into various allegations concerning Mr. Duhnke, none of which were substantiated, according to people familiar with the matter.

Republicans on the House Financial Services Committee last week asked the SEC and PCAOB to release the Pitt report. They also told the regulators to preserve all documents relating to Mr. Duhnke’s removal, accusing Mr. Gensler of treating the audit watchdog “like a political football.” The dismissal followed calls to replace the PCAOB board from Sens. Elizabeth Warren (D., Mass.) and Bernie Sanders (I., Vt.), as well as several progressive groups.

Jobs at the PCAOB command some of the highest salaries among regulators in the hope of attracting top talent in a high-paying field. In addition to the chair’s $672,680 pay, other board members are paid an annual salary of $546,900.

Write to Dave Michaels at dave.michaels@wsj.com and Jean Eaglesham at jean.eaglesham@wsj.com