WASHINGTON—President Donald Trump on Monday expressed frustration at the revision of his executive order temporarily banning travelers from several majority-Muslim countries from entering the U.S., seeking to blame the revised order, which he signed, on the Justice Department.

His comments, in a series of early-morning tweets, come at a delicate time for the president and the department, which is attempting to persuade the Supreme Court to revive the revised travel ban after lower courts blocked it on the grounds that Mr. Trump likely targeted Muslims in an unlawful way.

Mr. Trump has said his original executive order, which he signed Jan. 27, and the revised version, signed March 6, were intended to prevent potential terrorists from reaching U.S. soil.

“The Justice Dept. should have stayed with the original Travel Ban, not the watered down, politically correct version they submitted to [the Supreme Court],” Mr. Trump tweeted Monday. “The Justice Dept. should ask for an expedited hearing of the watered down Travel Ban before the Supreme Court - & seek much tougher version!”

The president’s tweets could complicate the Justice Department’s defense of the revised order. His remarks were welcomed by lawyers challenging the travel ban, while some of Mr. Trump’s supporters expressed worry.