Internet calling service Skype said its system was still down for around 20 percent of users on the second day of its biggest outage in more than three years, although service was gradually recovering.

Skype Chief Executive Tony Bates, facing his biggest challenge since being hired in early October, said Skype was focused on restoring the service and progress is going well.

He said Skype's group video chat and offline instant-messaging were still down but that the system was working for 80 percent of users of its core service, including free messaging, voice and video services between users, as well as low-cost calls to landlines.

Social network site Twitter was inundated with messages from users around the world commenting on Skype's problems, some applauding a recovery and others lamenting the extended outage.

The company, partly owned by Web retailer eBay Inc, counts around 124 million users, with some 25 million signed on at peak hours.

We do realize that we put our users through stress over the last 24 hours, Bates said, adding that the company was still investigating the cause.

He said the company had not yet assessed the financial impact from the outage, which comes as the company has been trying to expand its base of paying customers, including business clients looking for cheaper communications options.

We are looking for a form of compensation for our paying users, Bates said.

The company's last major outage occurred in August 2007 after a routine software upgrade.

Despite Skype's growing popularity, many consumers have been reluctant to cut off their landlines and rely solely on services like it due in part to questions about its reliability.

Such concerns, along with worries about online security, have slowed Skype's expansion into the business market.

It now also faces competition from rival online phone providers such as Google Inc and high-end videoconferencing tools like Cisco Systems Inc's umi service.

Bates replaced Joshua Silverman, an eBay executive who was CEO since early 2008. He was previously general manager of Cisco's enterprise, commercial and small business division.

In addition to fixing the outage, Bates faces the challenge of leading the company's expected initial public offering.

Skype is expecting to raise up to $1 billion in an initial public offering, sources familiar with the matter told Reuters last month. One source has said the IPO will likely come some time next year.

The company was founded in 2003, and online auction and e-commerce website eBay bought it in 2005 for $3.1 billion.

In November, eBay sold a majority stake to an investor group including Silver Lake, Canada Pension Plan Investment Board and Andreessen Horowitz for $1.9 billion in cash and a $125 million note. EBay retained a 30 percent stake.

(Editing by Steve Orlofsky)

Software Down