The justices denied the Nevada case and its attempt to substitute Deputy Attorney General Rod J. Rosenstein for Whitaker. The Maryland case is still before a federal judge there.

Goldstein and others say that Rosenstein, the Justice Department’s No. 2 official, should have succeeded Sessions and that it is unlawful for Whitaker to be running the department for even a short time.

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They brought the issue to the Supreme Court in a case initiated by Barry Michaels, who was challenging a law that prevents him from buying a firearm because of a previous nonviolent crime.

Maryland Attorney General Brian E. Frosh, in coordination with Goldstein, has also challenged the validity of Whitaker’s appointment as part of a pending case in federal court in Baltimore seeking to uphold a key section of the Affordable Care Act. U.S. District Judge Ellen L. Hollander has not yet ruled on the state’s motion to replace Whitaker with Rosenstein.

Hollander has not said when she will issue a decision, but the court’s action is expected to affect her decision.

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At a hearing in December, the judge suggested that a ruling invalidating Whitaker’s appointment would be inconsistent with past court decisions.

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“Wouldn’t I be an outlier if I agreed with you?” she asked Goldstein at the hearing.

Since the filings, Trump has nominated William P. Barr to replace Sessions as attorney general. His confirmation hearings in the Senate are scheduled to begin Tuesday.

The court took no action on a number of controversial cases that could transform its current term: Trump’s plan to end Deferred Action for Childhood Arrivals, the program known as DACA that protects some undocumented immigrants brought to this country as children; the administration’s directive to ban transgender service members in the military; restrictions on abortions in Indiana and on guns in New York City; and whether federal law forbids employment discrimination based on sexual orientation and gender identity.

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If the court does not act on these matters before Jan. 22, when it adjourns for a month-long break, the cases would probably not be added to the court’s docket this term.

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Also Monday, the court rejected a challenge to Montana’s limits on campaign contributions in state races. Challengers said the case presented “the exceptionally important question of whether Montana can stifle the voices of individuals, political committees, and political parties through very low contribution limits without any evidence of quid pro quo corruption.”

The U.S. Court of Appeals for the 9th Circuit upheld the limits, and Montana told the Supreme Court there was no reason for further review. It said there was no reason to force a state “to prove criminal bribery to support the state’s interest in a civil statute that limits — not bans — contributions to candidates for office.”

Justices also turned down a challenge to the constitutionality of the Consumer Financial Protection Bureau. At issue was whether the bureau’s structure gives its director too much power and the president too little in appointing and removing certain officials.