Cisco Systems Inc. sued Apple Inc. over the use of the iPhone name, setting up a trademark battle a day after the chief executive officer of Apple, Steve Jobs, introduced the new mobile device.

Cisco claims it owns the iPhone name for telephone service, and said yesterday in the complaint filed in San Francisco federal court that the Apple product “will share an identical sight and sound and strong similarity of meaning.” Apple called the suit “silly” and said it was confident it would prevail.

The lawsuit pits two of Silicon Valley’s biggest titans, Mr. Jobs and Cisco CEO John Chambers, against each other in one of the wireless industry’s fastest-growing areas, Web-enabled phones. The dispute surprised trademark lawyers who said it was inconceivable Apple would announce a product without having legal rights to the name.

“I don’t know what Cisco was asking for, but it would have to have been a heck of a lot for Apple to blow it off and risk a lawsuit,” a trademark lawyer with Darby & Darby in New York, Andrew Baum, said. “It’s pretty odd for a company to take this kind of risk.”

Shares of Cupertino, Californiabased Apple rose $4.43 to $97 at 4 p.m. New York time in Nasdaq Stock Market composite trading. Cisco gained 21 cents to $28.68. The suit was filed after the close of regular trading.

In the complaint, San Jose, California-based Cisco asked a federal judge to block Apple from using the iPhone name.

“We are the first company to use the name iPhone for a cell phone and if Cisco wants to challenge us on it we are very confident we will prevail,” Apple spokesman Steve Dowling said in an interview. “There are already several companies using the name iPhone for voice over IP products. We believe Cisco’s U.S. trademark registration is tenuous at best.”

Cisco has owned the iPhone trademark for six years. It bought the name as part of a 2000 purchase of InfoGear Technology Corp., and in January began selling a line of Internet-based cordless phones called iPhones.

The companies have been negotiating over the rights to the name as far back as 2001 without reaching an agreement. Cisco said it sent final documents to Apple on January 8 and hadn’t received a reply as of yesterday.

Cisco said it was unwilling to cede full rights to the name and couldn’t agree on terms that would let Apple proceed.

The complaint accuses Apple of a “surreptitious effort to attempt to obtain rights to use the name ‘iPhone’ in connection with the very products, telephones using cellular voice and data networks, for which it had asked Cisco for rights,” the complaint said.

A company called Ocean Telecom Services LLC filed an application with the U.S. Patent and Trademark Office for the name in September. Apple filed an application for the name iPhone in Australia. Both applications cite a third application, filed in Trinidad and Tobago, as being connected, Cisco said.

Cisco owns the rights to the name for “computer hardware and software for providing integrated telephone communication with computerized global information networks,” a broad category that could cover most phones, a trademark lawyer of McDonnell Boehnen Hulbert & Berghoff in Chicago, James M. McCarthy, said.

Apple may argue Cisco hasn’t used the name continuously since the trademark was issued in 1999, and that it has rights to the family of “I” products because of the popularity of the iPod digital music player and iBook computer, Mr. Baum said.

“It may be that Apple knows facts we don’t know that lead them to believe they are likely to win,” Mr. Baum said. “But the consequences of being wrong could be staggering.”

The case is Cisco Systems Inc. v. Apple Inc., 07-198, U.S. District Court for the Northern District of California.