WASHINGTON — The Defense Department’s inspector general said on Wednesday that it was investigating complaints that the acting defense secretary, Patrick M. Shanahan, had been promoting his former employer, Boeing, and disparaging its military contractor competitors.

The investigation will examine complaints filed last week by a watchdog group, Citizens for Responsibility and Ethics in Washington. Dwrena K. Allen, a spokeswoman for the inspector general’s office, said that investigators had informed Mr. Shanahan of the inquiry.

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Mr. Shanahan told lawmakers last week that he supported an investigation.

The investigation complicates what is already an uphill battle for Mr. Shanahan’s effort to become the next permanent defense secretary. As recently as last week, Defense Department officials believed that President Trump was about to formally nominate Mr. Shanahan for the job left vacant by Jim Mattis, who resigned in December.