The government rejected protests by some Danish opposition parties that said banning Quran burnings would infringe on free speech.
The decision to appoint a commission met with immediate scepticism from several political parties, including the government's support party, the anti-immigration Sweden Democrats.
Sweden's SAPO security service raised the terrorist alert from 3 to 4 on a scale from 1-5, reflecting a high threat.
The continuous repetition of insults against the Quran in Denmark and Sweden needs to end, and the authorities in both countries must confront these violations firmly and decisively.
Denmark is tightening border control due to security concerns after Quran burnings.
The move comes after Rabbi Menachem Margolin, chairman of the European Jewish Association (EJA), called on the Swedish government to take action against such vile acts.
The Danish government said it would seek to make legal changes that will ban Quran burnings.
Criticizing a religion or religious symbols is not punishable in Sweden; this falls under freedom of expression which is protected under the constitution.
"We can see how Russia-backed actors are amplifying incorrect statements such as that the Swedish state is behind the desecration of holy scriptures," Carl-Oskar Bohlin said.
Egypt summoned Sweden's chargé d'affaires to condemn incidents where copies of the Koran have been burned, the foreign ministry spokesperson said on Tuesday.