Users from Japan, Europe and the US all reported problems, which started at around 2030 GMT on 22 December.
The company said the fault had been caused by critical parts of its network being taken offline.
It is estimated that Skype was losing around half of its daily 20 million calls, when the problem first occurred.
A spokesperson for the firm confirmed the problem was ongoing but could not say how many customers were affected.
In a post the firm said that the problem had been caused by a series of supernode failures. These "act a bit like phone directories", the firm said, routing traffic between users.
"If you want to talk to someone, and your Skype app can’t find them immediately (for example, because they’re connecting from a different location or from a different device) your computer or phone will first try to find a supernode to figure out how to reach them," it read.
"Under normal circumstances, there are a large number of supernodes available. Unfortunately, today, many of them were taken offline by a problem affecting some versions of Skype."
This may take a few hours, and we sincerely apologise for the disruption to your conversations. Some features, like group video calling, may take longer to return to normal.
Skype is is one of the key applications of the modern world and any disturbance affects millions of life