Sun continues to pursue Apple Computer to get Java applications running on the iPhone, while another party is aiming at the same goal.

“We’ve expressed our intent to do this and our desire, really, to work with Apple to build a Java Virtual Machine (JVM) for the iPhone and we’re sort of moving forward with that,” said Sun vice president Eric Klein this week.

Apple has not yet responded publicly into having Java on its popular device. However, analysts are questioning if Apple’s iPhone SDK agreement would permit getting Java into the iPhone.

Sun is also reported to be working with Innaworks in hopes of bringing Java applications to iPhone.

“They’re actually working on a solution that allows developers to compile Java Micro Edition (Java ME) applications into native iPhone applications,” said Klein explaining that companies could submit these applications for inclusion in App Store.

Innaworks is planning to show its solution at the JavaOne conference to

be held in San Francisco next week, Klein said. According to the company’s press statement, Innaworks’ product, alcheMo for the iPhone is initially aimed at games publishers. Still in beta, alcheMo for iPhone was designed to use for the iPhone in porting Java ME mobile games to the iPod touch and iPhone without any manual adjustments. AlcheMo features an optimizing translator that converts Java applications code to the equivalent source code for the iPhone.

Since Sun wants to put the JVM on the iPhone via iPhone SDK, Apple and Sun need to discuss the clauses in the SDK license agreement.

“There’s no question one of our goals from the Java platform perspective is to allow our developers to get to as many phones as possible, and obviously, the iPhone has turned out to be a very successful platform, and we want to be on it,” said Klein stressing about Sun’s excitement on its plans. Meanwhile, Apple remains silent on the issue.