By Andrew Chung

NEW YORK, Dec 14 (Reuters) - Samsung took to the U.S. Supreme Court on Monday in a last-ditch effort to pare back the more than $548 million in damages it must pay Apple for infringing the patents and designs of the iPhone.

Samsung's petition must first be accepted for review by the Supreme Court. It is the latest step in a long-running patent lawsuit between the rival companies that epitomized the global smartphone wars.

Samsung Electronics Co Ltd was scheduled to pay $548.2 million to Apple Inc on Monday, according to papers filed with the a lower California federal court on Dec. 3. Samsung could not immediately confirm on Monday whether the money had been paid. A representative for Apple could not be reached.

In its petition to the high court, Samsung said it should not have had to make as much as $399 million of that payout for copying the patented designs of the iPhone's rounded-corner front face, bezel, and gridded icons.

It said that awarding total profits from the sale of its devices with those designs, even if they relate only to a small portion of the phone, allows for "unjustified windfalls" far beyond the inventive value of the patents.

"A patented design might be the essential feature of a spoon or rug. But the same is not true of smartphones, which contain countless other features that give them remarkable functionality wholly unrelated to their design," Samsung told the high court.

"Samsung is escalating this case because it believes that the way the laws were interpreted is not in line with modern times," the company said in a statement.

The South Korean electronics company's quest to limit damages to Apple stems from the $930 million judgment that followed a 2012 verdict for infringing Apple's patents and copying the iPhone's look.

In May, the U.S. Court of Appeals for the Federal Circuit in Washington, D.C., the nation's top patent court, stripped about $382 million from that total, saying the iPhone's appearance could not be protected through trademarks.

Another trial over remaining damages relating to some of Samsung's infringing products in the case is set to go ahead next spring.

In its petition on Monday, Samsung also told the Supreme Court that juries should not award damages on certain "functional" aspects of designs, such as flat screens, which allow for the reading of documents, or rounded corners, which make phones easier to slip into a pocket.

(Reporting by Andrew Chung; Editing by Alexia Garamfalvi and Dan Grebler)