WASHINGTON — The Supreme Court announced on Friday that it would hear a challenge to the leadership structure of the Consumer Finance Protection Bureau, agreeing to decide whether the president is free to fire its director without cause.

The bureau, the brainchild of Elizabeth Warren, then a law professor at Harvard and now a senator and presidential candidate, was created as part of the Dodd-Frank Act, which was passed in 2010 after the financial crisis. In an effort to protect the bureau’s independence, the statute said the president could remove its director only for cause, defined as “inefficiency, neglect of duty or malfeasance.”

That limit on presidential power has been repeatedly challenged in court by businesses that say it violates the separation of powers. The Trump administration agrees with the challengers. The bureau once took the opposite position, but it changed its stance in September, agreeing that its director could be fired at will.

Indeed, Kathleen Kraninger, the bureau’s director, urged the Supreme Court in a speech that month to hear a challenge to her own job security.