WASHINGTON—President Trump on Tuesday lit into Charles and David Koch, some of the Republican Party’s top donors, in a series of tweets, after their conservative donor network said over the weekend it wouldn’t financially back the party’s candidate for a North Dakota Senate seat.

“The globalist Koch Brothers, who have become a total joke in real Republican circles, are against Strong Borders and Powerful Trade. I never sought their support because I don’t need their money or bad ideas,” Mr. Trump wrote Tuesday. He went on to say that he has “made them richer,” referring to tax cuts he signed into law late last year and unspecified “Regulation Cuts” his administration has undertaken.

“Their network is highly overrated, I have beaten them at every turn,” he continued in a second tweet. “They want to protect their companies outside the U.S. from being taxed, I’m for America First & the American Worker -- a puppet for no one. Two nice guys with bad ideas. Make America Great Again!”

The Koch brothers’ network of about 500 conservative and libertarian donors met this past weekend in Colorado Springs. At the conference, leaders of the Koch-backed political and policy groups said they wouldn’t support Rep. Kevin Cramer, a GOP Senate candidate challenging Democratic incumbent Heidi Heitkamp, because he has sided with Mr. Trump on tariffs.

Mr. Trump won North Dakota by 36 percentage points in 2016, and Republicans see Ms. Heitkamp’s seat as one of their most promising pickup opportunities in the November midterms.