WASHINGTON — The White House adviser Kellyanne Conway’s public endorsement of Ivanka Trump’s product line appears to be “a clear violation of the prohibition against misuse of position,” and she should be disciplined, the federal government’s chief ethics watchdog wrote this week in a letter to the White House.

Although President Trump’s press secretary, Sean Spicer, said last week that Ms. Conway had been “counseled” about her statement, the White House has not clarified what that means. Experts in government ethics say that typically, offenses like Ms. Conway’s would result in a letter of reprimand, though it could be grounds for termination. It is up to the head of each agency — in this case, the president — to determine the punishment.

The Office of Government Ethics “has not yet received notification of any disciplinary or other corrective action against Ms. Conway,” Walter M. Shaub Jr., director of the office, wrote in a letter to Stefan C. Passantino, the deputy counsel to the president who is the designated ethics officer at the White House.

“There is strong reason to believe that Ms. Conway has violated the standards of conduct and that disciplinary action is warranted,” the letter said.