SAN FRANCISCO  Skype, the Internet calling service that has more than 400 million users around the world, is aggressively moving onto mobile phones.

The Luxembourg-based company, a division of eBay, plans to announce on Tuesday that it will make its free software available immediately for Apple’s iPhone and iPod Touch and, beginning in May, for various BlackBerry phones, made by Research in Motion.

Other companies have already made software for those phones that works with Skype, but it does not offer all of the service’s features.

As with Skype on the computer, users of Skype on mobile phones can make calls and send instant messages to other Skype users free, and they pay lower rates than the phone companies would charge when they use Skype to call landlines or other mobile phones.