UPDATE 3-Top court rejects U.S. govt's oil royalty appeal

* Case concerned Anadarko leases in Gulf of Mexico

* Company said issue involved dwindling number of leases

By Jim Vicini and Ayesha Rascoe (Adds comments from Interior Secretary Salazar)

WASHINGTON, Oct 5 (Reuters) - The Supreme Court rejected on Monday an Interior Department appeal of a ruling that the government says will likely cost it at least $19 billion in lost oil royalties from energy companies.

The justices declined to review a ruling by a U.S. appeals court that Anadarko Petroleum Corp (APC.N) did not have to pay about $350 million in royalties for drilling on federal leases in the Gulf of Mexico issued between 1996 and 2000.

The decision in Anadarko's favor could lead other energy companies to forego paying royalties and cost the United States at least $19 billion in foregone or refunded royalties, the Justice Department said in its appeal on behalf of the Interior Department.

Justice Department attorneys argued that the appeals court incorrectly interpreted the royalty relief law and said the amount of money at stake makes the case worthy of Supreme Court review.

"Whatever the precise amount of forgone future royalties proves to be, the total cost will be huge and it will have a direct adverse affect on the Treasury," Solicitor General Elena Kagan said in the appeal, adding that the companies would get "unjustified windfalls."

The Supreme Court rejected the appeal without comment.

The dispute centered on financial incentives Congress gave energy companies in the 1990s, when oil prices fell to $10 a barrel. To make drilling in the deeper waters of the Gulf of Mexico more economically feasible, royalties were waived on initial oil and natural gas production.

Interior Secretary Ken Salazar pointed out that previous administrations took the position that if oil and gas prices rose to a certain level, the royalty relief should end for these leases.

"In my view, they were correct," he said in a statement.

Kerr-McGee Corp, which was bought by Anadarko in 2006, sued the department, arguing it did not have the authority to take away the royalty relief provided by Congress.

The Supreme Court's decision "preserves the sanctity of law and brings resolution to this issue," said Anadarko Petroleum spokesman John Christiansen.

"Eight different federal judges and four federal courts reviewed and interpreted the Deep Water Royalty Relief Act, and every one concluded that we acted in accordance with the law," Christiansen added.

Anadarko has said the clear intent of Congress was "to assure that companies were afforded the royalty treatment it granted as encouragement to make huge investments in the deepwater Gulf of Mexico frontier."