WASHINGTON—President Donald Trump is set to announce plans to expedite construction of a wall along the Mexican border, and is preparing orders that ban people from countries deemed a terror risk from entering the U.S. as well as suspend the U.S. refugee program.

Mr. Trump plans to travel Wednesday to the Department of Homeland Security, where he said he would be announcing his border-security plans. He will also include an order aimed at punishing so-called sanctuary cities where law-enforcement officials limit cooperation...