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Google Jan. 26 rolled out an HTML5-based version of its popular Google Voice application for Apple’s iPhone several months after Apple rejected Google’s original submission to its App Store.

Google Voice is a Web-based phone management application that lets users route calls to their home, work and mobile phones from a special Google granted number. The free Web app, which also lets users make low-cost long-distance calls, has been incredibly popular since Google began slowly rolling it in June and has more than 1.4 million users.

Google software engineers wrote a version of Google Voice for the iPhone platform and submitted it to the App Store in June, only to have it rejected for competing with iPhone’s SMS and dialing features.

That app was designed as a native program for the iPhone, meaning it would be downloaded directly the devce. When Apple rejected it, it prompted an inquiry from the Federal Communications Commission and fueled Google to write a version anyone may access through a mobile Web browser.

That version is now live for both the iPhone OS 3.0 and higher and smartphones based on Palm’s WebOS, Google said via a blog post. Based on the vastly improved HTML5 Web markup language, the app’s AppCache will let users interact with Web apps without a network connection and store data locally on the device.

The app will let Google Voice users do pretty much what they can do with the desktop version of the app, including listen to voicemail and read voicemail transcripts, send and receive text messages, and make inexpensive international calls.

Users can also add shortcuts to Google Voice features such as the Dialer, Compose SMS, Inbox or Contacts, to their iPhone home screen or Palm launcher.

The new Web app also lets users display their Google Voice number as the outbound caller ID so that return calls come back to their special Google Voice number.

Users must have a Google Voice account and a voice plan on a cell phone to place calls with the app. Those who want to try the app can point their browser to and sign in to their Google Voice account. Google Voice is still available in the U.S. only.

The Google Voice app represents a definite workaround to Google’s standoff with Apple’s App Store, which is incredibly strict if not inconsistent in its treatment of submissions. The App Store has been known to accept and summarily bounce apps that fail to meet its rigid requirements for quality and other criteria.

Google and Apple are increasingly competing online, particularly on the mobile front. Google Jan. 5 launched the Nexus One smartphone, which many liken to Apple’s iPhone.

Meanwhile, Apple has acquired Web properties such as music provider LaLa and mobile ad maker Quattro Wireless, ostensibly to compete with Google and others in the mobile Web cloud.