Problems arose when a web server used by gamers was attacked and its traffic got transferred to Telia's servers.
Telephone and internet services were affected on Tuesday and Wednesday with many people experiencing slow connections and some unable to get online at all.
Telia says it managed to tackle the problem by around 10pm on Wednesday, although some people were still reporting problems on Thursday morning.
"We cannot get into specific details about what we we did last night, but we put some technical arrangements in place to ensure it won't happen again," Marcus Haglund, a press officer for Telia, told The Local on Thursday.
"We don't see any problems right now that are connected to the attack so if people are experiencing issues again, it could be something else," he added.
Over five million Swedes use Telia to provide their home phones, TV and mobile services. The company is part-owned by the Swedish state.
Many angry users managed to use their 3G connections to get on to Twitter to complain about the connection problems they were experiencing on Wednesday.
Our internet (wi-fi) has been down for hours now… #telia what's going on?
— Felix Martinsson (@Felixmartinsson) December 10, 2014
— Micha Toma (@spoof79) December 10, 2014