Speaking at a seminar on Monday on the occasion of the tenth anniversary of the terror attacks on the US on September 11th 2001, Danielsson said that the strength of al-Qaeda had been greatly weakened in recent years.
The threat from al-Qaeda could be complicated if the organisation divides into regions, according to Malena Rembe, an analyst at Säpo.
"It doesn't make the job easier for us," she said.
The September 11th attacks may in retrospect be seen as a culmination of al-Qaida's capabilities, Danielsson said.
The attack was also unique in that it coincided with the age of mass communication, and so it could be witnessed live.
"This contributed to the scare factor," the Säpo director said.
The worldwide broadcast of the second plane crashing into Manhattan's World Trade Centre ensured that the propaganda effect was maximised.
"However, similar attacks have not occurred is not because al-Qaeda has not tried. Counter-terrorism is difficult," Danielsson said.
"To ward off threats takes as long as finding out whether the threats are not true."
Säpo's mission is furthermore to prevent terrorist crimes, Danielsson underlined.
"Our mission is not to get convictions for terrorist crimes, that is not a measure of our effectiveness," said Danielsson.
"We can and are likely to be exposed to terrorist attacks again. But it will not destroy our democratic system. Terrorism rarely does, even though it may seem that way."