The government says desecrating Islam's holy book can fuel extremism and have negative geopolitical impacts.
Denmark announced on Sunday it was considering banning Quran-burning protests, which have created tensions with the Muslim world.
Islam's holy book has been desecrated at several demonstrations in Sweden and Denmark recently, fraying diplomatic relations between the pair and several Middle Eastern countries.
The Danish government claims the stunt plays into the hands of extremists and sows division, though defenders see it as a necessary - yet unsavoury - part of freedom of speech.
The authorities want to "explore" the possibility of stopping situations where "other countries, cultures and religions are insulted", especially if they have "significant negative consequences for Denmark... particularly in terms of security," the foreign ministry wrote in a statement.
"This must of course be done within the framework of freedom of expression protected by the constitution," it added, stressing such liberty was one of Denmark's most important values.
At the end of June, Salwan Momika, a 37-year-old Iraqi refugee in Sweden, set fire to the Quran outside Stockholm's main mosque.
Last week, he again stomped on and tore up a copy of the book outside the Iraqi Embassy to show his opposition to the faith.
The incident caused a diplomatic spat with Egypt, Saudi Arabia and Iran which summoned Swedish diplomats. Algeria also recalled the representatives of Denmark.
Hundreds of Iraqis also invaded and set fire to the Swedish embassy in Baghdad as a result of the incident.
The Swedish ambassador was expelled from Iraq, while Iran has indicated it will not accept a new ambassador from the Scandinavian country on its territory.
The Danish Foreign Ministry notes Quran-burning protests have "reached a level where Denmark, in many parts of the world, is perceived as a country that facilitates the insult and denigration of the cultures, religions and traditions of other countries."
The "main purpose" of some of these demonstrations is to provoke and "could have important consequences", it claimed.
Denmark's far-right has also seized on rancour, with the Danske Patrioter movement posting a video of a man desecrating and burning what appears to be a Quran.
Trying to copy the previous incident, nearly a thousand demonstrators gathered at night in Baghdad and tried to walk towards the Danish embassy, but Iraqi police dispersed them with truncheons and tear gas.
In a separate statement, Swedish Prime Minister Ulf Kristersson said on Sunday he had been in close contact with his Danish counterpart Mette Frederiksen, adding Sweden was mulling something similar.
"We have also started to analyse the legal situation in order to consider measures to strengthen our national security and the security of Swedes in Sweden and around the world," Kristersson recalled on Instagram.
Sweden on Thursday ordered its police and military to strengthen their preparations against terrorism amid deteriorating security.