Denmark is considering banning protests involving burning the Koran 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.