(Reuters) - The chief executives of Apple Inc and Samsung Electronics Co Ltd were summoned for court-directed mediation on Monday over the iPhone maker's claims the Korean firm has "slavishly" copied some of its products.

Apple's Tim Cook and Samsung's Choi Gee-sung were instructed by a federal judge to appear for a two-day mediation to help resolve the bitter patent litigation between the two companies.

There was no sign of either CEO at the San Francisco federal courthouse on Monday. The mediation session had been on a magistrate judge's calendar for Monday morning, but the meeting - which is not open to the public - could have been arranged at an undisclosed location, such as a law firm office.

Representatives from Apple and Samsung declined to provide any details on Monday about the meeting.

The U.S. case, the most closely watched in a global patent war between the two companies involving some 20 cases in 10 countries, is set for trial at the end of July in San Jose, California. Each company denies the other's allegations of patent infringement.

Apple, the maker of the iPod, iPad and iPhone, has a complex relationship with Samsung, a conglomerate that makes computer chips, Galaxy smartphones, and televisions.

While Samsung's smartphones and tablet computers run on Google's Android operating system and compete with Apple's products, Samsung is also a key components supplier to Apple.

The U.S. company, which investors value at close to $600 billion, has accused Samsung of "slavishly" copying the iPhone and iPad through products that run on Android. Samsung, which has a stock market value of about $161 billion, has counter-sued with claims accusing Apple of infringing its patents.

Both companies have a lot at stake. Their share prices hit record highs this year as they reported soaring profits, partly fueled by their dominant position in the smartphone sector.

Samsung sold 44.5 million smartphones in the first quarter of 2012, giving it a 30.6 percent share of the global high-end market. Apple's sales of 35.1 million iPhones gave it a 24.1 percent share.

"BIG GAP"

On Sunday in Seoul, the head of Samsung's mobile division said the South Korean company wanted to resolve differences with Apple.

"There is still a big gap in the patent war with Apple," JK Shin said, before departing for the U.S. mediation talks. "But we still have several negotiation options."

Apple spokeswoman Kristin Huguet reiterated a prior statement, saying Apple needs to protect its IP against "blatant copying."

An eventual Apple and Samsung settlement could have wider implications because the U.S. company is locked in disputes with major Android phone makers HTC Corp of Taiwan and Motorola Mobility Holdings Inc of the United States.

Court documents show Apple and Samsung have had at least one mediation session, although it is not clear if Cook and Choi were involved. The latest mediation session will be overseen by U.S. Magistrate Judge Joseph Spero. He declined to comment.

Cook became Apple's CEO last year, taking over from the company's co-founder and inspiration, Steve Jobs, who had told his biographer he intended to go "thermonuclear" on Android. Jobs died in October after a long illness.

Cook has echoed Jobs' mantra that Apple's top priority is to make "great products" but he has also made his mark by revealing the U.S. company's production partners and initiating investigations into allegations of labor abuses in its supply chain.

Choi, 61, became Samsung's leader in 2010, after more than three decades with the company. He is seen as a mentor to Jay Lee, the only son and heir apparent of Samsung Chairman Lee Kun-hee. Choi, asked by reporters on Sunday about the court mediation, declined to comment.

U.S. courts are increasingly demanding parties in civil disputes try mediation, although success if far from certain.

Last year, Oracle's Larry Ellison and Google's Larry Page undertook mediation in an intellectual property fight over Android, but no settlement was reached and a trial in the case has entered its sixth week.

"I can't imagine that the heads of a major enterprise of that kind would take any more seriously a decision of that magnitude, simply because they are in the room together," said Vaughn Walker, a former northern California federal judge who now works as a mediator.