The notes, which are signed ISIS and carry the terrorist organisation's flag, threaten to decapitate 'non-believers' unless they become a Muslim or pay a religious tax.
They have been distributed among several cities including Stockholm and warn 'the police will not save you from being murdered'.
According to Daily Mail translated, the notes said: ' You who are not believers will be decapitated in three days in your own house. We will bomb your rotten corpses afterwards.
'You must choose between these three choices: 1. Convert to Islam. 2. Pay the jizya [religious tax] for protection. 3. Or else, you will be decapitated.
The notes promised attacks within three days and were posted last Thursday (December 10), in areas including Ronneby, Sigtuna and Västerås with officers on patrol in the latter over the weekend to ensure no one acted on them.
'The police will not prevent or save you from you being murdered. (Death comes to all of you).'
Swedish radio stations reported police were investigating the new threats and comparing them to previous warnings of violence.
Emil Andersson, police chief in Sigtuna, around 30 miles north of Stockholm, told Radio Uppland the threat was being taken seriously and officers were increasing security measures.
He added the Swedish intelligence agency was also involved in the investigation and examining the symbols and language used in the letters.