The House Armed Services Committee on Thursday asked Defense Secretary Lloyd J. Austin III to testify next month about why he and his aides kept secret from the White House for several days that he was hospitalized after having complications from prostate cancer surgery.

The committee chairman, Representative Mike D. Rogers, Republican of Alabama, said that “Congress must understand what happened and who made decisions to prevent the disclosure of the whereabouts of a cabinet secretary.”

Mr. Rogers said that he scheduled a hearing for Feb. 14 after he accused Mr. Austin of evading important questions about the secretary’s hospitalization during a recent phone call between the two men.

“Specifically, I am alarmed you refused to answer whether you instructed your staff to not inform the president of the United States or anyone else of your hospitalization,” Mr. Rogers said in a letter to Mr. Austin that the committee made public on Thursday night. “Unfortunately, this leads me to believe that information is being withheld from Congress.”

Mr. Austin was released on Monday from Walter Reed National Military Medical Center in Bethesda, Md., and has been working at home while he recuperates. Top Pentagon aides have been eager to try to put the episode behind them, seeking to portray a back-to-work image, albeit from home, for their boss by issuing statements that he spoke by phone this week with his counterparts from Ukraine and Israel.

But there is little chance the issue will fade away soon. Lawmakers and senior administration officials say that Mr. Austin’s handling of the matter has damaged his credibility with President Biden and Congress, and that it raises questions about the overall competence of his department in dealing with the self-made crisis. All of that is now the subject of a 30-day internal department review, as well as an investigation by the Defense Department inspector general.

Mr. Austin, a 70-year-old retired Army general, was in severe pain and rushed by ambulance to Walter Reed on Jan. 1. He was put in intensive care after complications from a prostate removal surgery he underwent on Dec. 22.

But several top Pentagon officials did not learn of the secretary’s hospitalization until the next day, Jan. 2. The White House was not notified until Jan. 4, a major breach of protocol at the highest national security levels. Further complicating matters, neither Pentagon nor White House officials learned until Jan. 9 that Mr. Austin had been diagnosed with cancer in early December.