WASHINGTON — The Supreme Court agreed on Tuesday to decide whether high-ranking George W. Bush administration officials — including John Ashcroft, the former attorney general, and Robert S. Mueller III, the former F.B.I. director — may be held liable for policies adopted after the Sept. 11 attacks.

The case began as a class action in 2002 filed by immigrants, most of them Muslim, over policies and practices that swept hundreds of people into the Metropolitan Detention Center in Brooklyn on immigration violations in the weeks after the attacks. The plaintiffs said they had been subjected to beatings, humiliating searches and other abuses.

The roundups drew criticism from the inspector general of the Justice Department, who in 2003 issued reports saying that the government had made little or no effort to distinguish between genuine suspects and Muslim immigrants with minor visa violations.

A divided three-judge panel of the United States Court of Appeals for the Second Circuit, in New York, let the case proceed last year.