WASHINGTON—The White House on Monday will embark on a three-week messaging campaign aimed at refocusing attention on President Donald Trump’s agenda and framing a debate later this summer over rewriting the U.S. tax code.

The “Made In America” campaign, which starts with the president highlighting locally made products from around the country, is the latest attempt by Mr. Trump’s communications team to control a narrative that has consistently spun out of their grasp during the six months since the inauguration.

...