What can a government official do if a newspaper publishes a story criticizing the President?

The government official can write a letter to the editor.

Explanation:

The first amendment of Untied States gave the people with the freedom of speech. This protected journalists  so they can openly criticize the government without having to fear that the government will retaliate and hurt them.

The only thing that the government can do is to communicate in a civil manner with the newspaper editor if there's any misunderstanding within the story. If the government can provide enough proof that the criticism wasn't true, the publisher will be pressured by the public if they didn't edit their piece.