The court said Thursday that the “honest services” law could not be used in convicting Mr. Skilling for his role in the collapse of Enron. But Justice Ruth Bader Ginsburg said in her majority opinion that the ruling does not necessarily require Mr. Skilling’s conviction to be overturned.

During arguments in December and March, several justices seemed inclined to limit prosecutors’ use of this law, which critics have said is vague and has been used to make a crime out of mistakes and minor transgressions in the business and political world.

The court, at the same time, rejected Mr. Skilling’s assertion that he did not get a fair trial in Houston because of harshly critical publicity surrounding the case in Enron’s hometown.

The court in this ruling also sided with the former newspaper magnate, Conrad Black, setting aside a federal appeals court decision that had upheld Mr. Black’s honest services fraud conviction. But as in Mr. Skilling’s case, the justices left the ultimate resolution of the case to the appeals court.

The justices also threw out an appeals court ruling against Bruce Weyhrauch, a former Alaska legislator who is facing charges under the honest services law.

Thursday’s ruling could affect the continuing prosecution of Rod Blagojevich, the former Illinois Governor, and the convictions of Don Siegelman, the former Alabama Governor, and Richard Scrushy, the former chief executive of HealthSouth.

The government argues that both Mr. Skilling’s and Mr. Black’s convictions should be sustained, even with the court’s ruling Thursday.

Lawyers for the two men say that the entire case against them should be thrown out.

Mr. Skilling was convicted in 2006 on 19 counts of conspiracy, securities fraud, insider trading and lying to auditors for his role in the downfall of the once-mighty Enron. The company collapsed into bankruptcy in 2001 under the weight of years of illicit business deals and accounting tricks. Mr. Skilling is serving a sentence of more than 24 years at a minimum security prison outside Denver.

Mr. Black, serving a 6 1/2-year prison term, and two other former executives were convicted of depriving the Hollinger International media empire of their faithful services as corporate officers. The company once owned The Chicago Sun-Times, The Daily Telegraph of London, The Jerusalem Post and hundreds of community papers across the United States and Canada.

Central to the case is $5.5 million that the defendants say were management fees they were owed and were trying to collect in such a way that they would not have to pay Canadian income tax. The government says the money belonged to the company’s shareholders.

Mr. Weyhrauch wants charges against him dropped. Prosecutors allege that he failed to disclose he was in job negotiations with an oil-field operations company at the same time the state legislature was also considering an oil bill. But Mr. Weyhrauch says disclosure was not required by Alaska law. He wants the court to bar a federal honest services fraud prosecution without an allegation of a violation of state law as well.