US Defence Secretary Lloyd Austin was hospitalised earlier this week due to complications from a medical procedure, the Pentagon said Friday, at a time when Washington is facing a growing crisis in the Middle East.

Austin was admitted to Walter Reed National Military Medical Center on the evening of January 1 "for complications following a recent elective medical procedure," Pentagon Press Secretary Major General Pat Ryder said in a statement, without providing details on the complications or the duration of the hospital stay.

"He is recovering well and is expecting to resume his full duties today," Ryder said.

The Defence Department had not previously disclosed that Austin was hospitalised, with Friday's announcement prompting criticism from the Pentagon Press Association.

In a letter to the Pentagon press secretary expressing "significant concerns," the press association said withholding the announcement for days until "late on a Friday evening is an outrage."

"The public has a right to know when US Cabinet members are hospitalised, under anesthesia or when duties are delegated as a result of any medical procedure," said the letter from the association, made up of journalists that cover the Pentagon.

The secretary's hospitalisation comes with tensions soaring in the Middle East.

On Thursday, the United States carried out a strike that killed an Iran-backed commander in Baghdad whom the military accused of involvement in attacks on American forces, infuriating the Iraqi government.

"At all times, the deputy secretary of defence (Kathleen Hicks) was prepared to act for and exercise the powers of the secretary, if required," Ryder said.

A Defence Department spokesperson later told AFP that the deputy secretary "is automatically authorised to perform the duties of the secretary if he is unable to perform them," and that "she did make some routine decisions on his behalf this week."

Austin was aware of the Baghdad strike, the spokesperson said, adding that the secretary and US President Joe Biden had previously authorised the action.