WASHINGTON — Federal regulators have given preliminary approval for a cryptocurrency venture tied to President Trump and his family to operate a digital-asset bank, a decision that has drawn immediate condemnation from Senate Democrats who are now pushing legislation to bar such an action.

Sen. Elizabeth Warren (D-Mass.), the top Democrat on the Senate Banking Committee, and nine other Senate Democrats introduced a bill Saturday that would bar the president, the vice president, their immediate family members and other senior government officials from owning or controlling banks.

The measure was proposed a day after the Office of the Comptroller of the Currency — which is part of the Trump administration — granted conditional…