Denmark is considering banning protests involving burning the Quran or other religious texts over security and diplomatic concerns.
The Danish foreign ministry said whilst protecting freedom of expression is crucial, such protests benefit extremists and pose a security threat.
Copenhagen is looking at legal means to intervene in some circumstances, including protests outside embassies.
Sweden's prime minister also said work on a similar process has begun there.
Both Scandinavian countries have come under pressure in recent weeks, after authorities gave permission for a series of controversial protests where Islam's holy book was destroyed, stoking diplomatic tensions with several Muslim-majority nations.
In its statement, Denmark's foreign ministry said it wants to explore intervening in some protests where "other countries, cultures, and religions are being insulted, and where this could have significant negative consequences for Denmark" - including security concerns.
But the Danish government emphasised free speech was a fundamental value and any change must be done "within the framework of the constitutionally protected freedom of expression and in a manner that does not change the fact that freedom of expression in Denmark has very broad scope".
The statement also specifically acknowledged the impact these controversial protests have had on Denmark's international reputation, repeating the government's earlier condemnation of burning religious texts.
These protests have reached a level where Denmark "is being viewed as a country that facilitates insult and denigration of the cultures, religions, and traditions of other countries" in many parts of the world, it added.