Tom Steyer, a billionaire California investor who spent more than $91 million supporting Democrats in the 2016 elections, issued the demand to his party in a letter on Wednesday. In his message, Mr. Steyer described Mr. Trump as a “clear and present danger to the republic” and called on Democrats to pledge that they would seek to remove him from office if they take control of Congress next year.

Mr. Steyer — who is considering a run for Senate, perhaps against Senator Dianne Feinstein, a fellow Democrat — cited a range of acts by Mr. Trump to justify impeachment, including the president’s “relationship with Vladimir Putin and Russia,” allegations that Mr. Trump has used the presidency to “promote his own business interests” and his “seeming determination to go to war.”