Internet telephony firm Skype took a second major leap into the wireless market in just a few weeks, unveiling software from top phone maker Nokia Oyj which could run on more than 200 million smartphones around the world.

The new Skype for Symbian software is available for free download from Nokia's Ovi Store to consumers globally.

Skype made its first major leap into cellphones in mid February, striking a deal with the largest U.S. mobile carrier Verizon Wireless.

Skype's free calls on computers have become an Internet phenomenon since start in 2003 and it has some 520 million registered users around the globe. But so far it has made little progress in wireless, as most telecoms operators have seen it as a risk to their core business of voice calls.

Nokia said it was seeing in total around 1.5 million downloads a day from Ovi Store, compared with around 1 million three months ago.

(Editing by David Holmes)