Shares of Pandora Media Inc. rose the most in more than a month as the prospect of competition from Apple Inc. receded after the iPod maker unveiled no music product at an event Tuesday.

Stock of Pandora, based in Oakland, California, climbed 8.4 percent to $9.86 in New York for the biggest intraday gain since Aug. 30. The Internet radio company was the biggest gainer in the Russell 1000 Index.

“This is likely a relief rally for Pandora shares,” James Marsh, an analyst at Piper Jaffray, said in an e-mail. “The most likely timing would be at the next iPod event, probably 10 months from now. So Pandora shares likely have some reprieve from Apple’s threat, at least in the short term.”

Apple, at the event in San Jose, California, highlighted new products and services including a smaller version of the market-leading iPad tablet. While introducing the new tablet, Phil Schiller, Apple’s senior vice president of global marketing, said Pandora looks and works great on the device.

Apple is negotiating with record labels for the rights to start an advertising-supported streaming radio service, people with knowledge of the plans said in interviews last month.