Noah Bookbinder, CREW’s executive director, said he was pleased that the agency reached this conclusion.

“The law is clear that government officials can’t use their official positions for political or campaign activity,” Mr. Bookbinder said on Friday, after his organization released the letter. “It is important to maintain real lines between government and politics and the Office of Special Counsel’s position makes clear they are going to be active to protect those lines.”

The White House did not immediately respond to a request for comment.

This is the second time a White House official has been reprimanded for apparently violating federal law, with Kellyanne Conway being rebuked in February by the Office of Government Ethics for urging the public to buy fashion products sold by Ivanka Trump’s brand.

The federal law puts no limits on the ability of federal officials to take positions that are critical of policies supported by others.

But a federal official may not use his or her official position, while on duty, or in a federal workplace, to urge a particular political outcome, like the ouster of Mr. Amash, or use it to raise money for a political cause, which led the Citizens for Responsibility and Ethics group to also file a complaint against Mr. Amash with the Office of Congressional Ethics, which has jurisdiction over members of the House.

A violation of the Hatch Act can result in a letter of reprimand, a civil fine of up to $1,000 or the suspension, demotion or even the removal of a federal employee, with enforcement powers generally vested in the United States Merit Systems Protection Board, if a charge is raised by the Office of Special Counsel, for individuals like Mr. Scavino who is not confirmed by the Senate.