In an e-mailed statement, Adobe said it had evaluated the iPhone software development kit Apple had released March 6 in beta, and could now "start to develop a way to bring Flash player to the iPhone."
The latest comment casts some doubt on whether Adobe is in the process of building such a player. Flash is the most widely used technology for playing online video through a Web browser.
Apple was not immediately available for comment.
During a conference call with investors Tuesday, Narayen said company developers had downloaded Apple's SDK and were ready to build a player.
"We believe Flash is synonymous with the Internet experience, and we are committed to bringing Flash to the iPhone," Narayen said, according to The Wall Street Journal. "We have evaluated (the software developer tools) and we think we can develop an iPhone Flash player ourselves."
Apple chief executive Steve Jobs recently told a shareholders meeting that available versions of the Flash player were too slow to be useful in the iPhone. Adobe's response at the time was that the iPhone wasn't ready for the Web without the company's popular technology.
Rather than support Flash, Apple requires that video be delivered in a particular file format. As a result, even though Google's YouTube has agreed to go along with Apple, only a fraction of Web video is playable on the iPhone. Flash is used to display the majority of online video, including that on YouTube.
Adobe would like to get Flash on the iPhone because of the gadget's growing popularity. The iPhone is second only to the BlackBerry in smartphone sales in the United States.
Apple's release of an iPhone SDK is part of the company's strategy to open up the device's software platform to third-party developers. Before the SDK, developers were restricted to building applications that could only run in the iPhone's Web browser.
In June, Apple plans to release a new version of the iPhone operating system. The upgrade will have the necessary hooks for tying SDK-built apps to the OS.
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