Swedish police say they have arrested three men in the capital, Stockholm, on suspicion of preparing terrorist acts and financing terror groups.
Swedish police did not say how the raid was linked to the Norway case
Earlier on Thursday, Norwegian police said they had arrested three people in the Norwegian capital, Oslo, on suspicion of financing terrorism.
The arrests were part of a co-ordinated operation, Swedish police said.
It said the three men held in Stockholm were Swedish citizens and that they were arrested at separate addresses.
Some reports suggest the men are suspected of involvement in financing and planning acts of terrorism in Somalia.
The Norwegian police security service (PST) did not identify the suspects, saying only that one or more of them faced a detention hearing in court.
Norwegian media reported that the suspects held in Oslo were of Somali origin.
'No cartoon link'
A spokesman for Sweden's security police (Saepo), Jakob Larsson, urged people to remain calm, saying there was "nothing to indicate that any act of terrorism is being planned in Sweden - against Sweden, so to speak".
He confirmed that the arrests had been co-ordinated with the PST.
He also said there was no connection with Swedish artist Lars Vilks or the Muhammad cartoons.
Last year a cartoon by Mr Vilks showing the Prophet Muhammad's head on a dog's body led to death threats against him.
Earlier there were riots in several Muslim countries over Danish cartoons of the Prophet Muhammad, first published in September 2005 by Jyllands-Posten newspaper.