"For several years it has been discussed whether we can do anything about certain religious preachers undermining democracy, basic freedoms and human rights, and integration," Denmark's church minister, Bertel Haarder, said in a statement.
"We have now shown that we can," he added.
The new rules will make it a criminal offence for preachers to give their "explicit approval" to criminal acts -- such as killings, rape and bigamy -- as part of religious education, which will be punishable with a fine or up to three years in prison.
Denmark will also establish a public list of preachers "with views and values contrary to fundamental Danish values" who will be banned from entering the country.
If they are EU citizens, who enjoy freedom of movement within the bloc, they will be put on a separate "observation list" which will not be open to the public.
The government said the measure had the backing of a majority of lawmakers and is set to put the proposals to parliament after the summer break.
Critics said the new rules risk having unintended consequences.
Extremist views "do not disappear because you ban them. Instead there is a risk that they become more exciting and appealing because they are prohibited," Pernille Skipper, spokeswoman for the leftist Red-Green Alliance (Enhedslisten), told daily Jyllands-Posten.
Earlier this year a Danish documentary series titled "The mosques behind the veil" prompted a heated debate after using a hidden camera to show how some imams in the country supported illegal practices such as the stoning of women and corporal punishment of children.
The documentary was controversial, with some Danish Muslims claiming it painted an unfair picture of the country's mosques, while others said it reflected real problems that needed to be addressed.