“One of the reasons for the increase is that the Security Police have received concrete information and made a judgment that we need to act within the framework of our counter-terrorism operations,” SAPO said in a statement.
Level four means that there is a high probability that “persons have the intent and ability to carry out an attack”.
Prosecutors have opened a preliminary investigation into a possible terrorist offense, indicating the raised level was not due to a generalized risk assessment.
Danish police also said on Wednesday they had increased their security readiness to the second-highest of five levels of readiness, as a consequence of the attacks in Paris last week.
Local Swedish news agency Six, citing an unnamed source, said an Iraqi man, trained in Syria, entered Sweden on Wednesday with the intent to carry out an attack.
The agency said authorities did not know where, when or how any attack could be carried out. It was not clear whether the attack was planned to be carried out in Sweden.
The security police declined to comment about the report.
Sweden over the last few years has participated in NATO missions in Afghanistan and are training Kurdish forces in Iraq, moves that have changed its traditional image of neutrality.
The last militant attack in Sweden came in 2010 when a suicide bomber died when his bomb belt went off prematurely in central Stockholm as he was getting ready to attack a train station or department store.
The same month Swedish and Danish police arrested five people for planning to attack employees of a Danish newspaper that sparked global controversy in 2005 with cartoons of Prophet Mohammad.