A new lawsuit accuses President Trump, his company and three of his children of using the Trump name to entice vulnerable people to invest in sham business opportunities.

Filed in federal court in Manhattan on Monday, the lawsuit comes just days before the midterm elections, raising questions about whether its timing is politically motivated. It is being underwritten by a nonprofit whose chairman has been a donor to Democratic candidates.

The allegations take aim at the heart of Mr. Trump’s personal narrative that he is a successful deal-maker who built a durable business, charging he and his family lent their name to a series of scams.

The 160-page complaint alleges that Mr. Trump and his family received secret payments from three business entities in exchange for promoting them as legitimate opportunities, when in reality they were get-rich-quick schemes that harmed investors, many of whom were unsophisticated and struggling financially.