The Danish prime minister has met members of a new association called "Democratic Muslims" in a fresh effort to defuse the Muhammad cartoons row.
Danish embassies in Muslim countries have been targeted
Protests took place in Turkey over the weekend, while Denmark saw about 25 Muslim graves desecrated in what police called a "backlash" against the uproar.
Vandals smashed only Muslim headstones in Esbjerg, west of Copenhagen.
The group meeting Anders Fogh Rasmussen on Monday was set up by MP Naser Khader to counter extremism.
The BBC's Thomas Buch-Andersen in Copenhagen says the group claims to represent around 80% to 85% of Muslims in Denmark.
He says that although that may be a high claim, there is no doubt they represent the majority of the country's 200,000 Muslims.
There has been criticism that Prime Minister Rasmussen is meeting Mr Khader's "Democratic Muslims" network and not other Muslim groups.
"The objective of the meeting is to start a dialogue with Danes of Muslim faith about, among other things, integration and the current situation," said a statement from the prime minister's office, quoted by the AFP news agency.
Mr Khader set up the network earlier this month in response to the outrage over the 12 cartoons of the Prophet Muhammad which were first published in a Danish newspaper.
He said it was time for "dialogue, rather than digging trenches" and called on Muslim countries, Danish imams and the government to enter into talks.
"Only by uniting can we change the fundamentalistic picture of Islam that the many extremists have drawn with violence," he said.
The international turmoil that has followed the publication of the cartoons and their reproduction in the European press led Denmark to withdraw diplomats from the Indonesian capital Jakarta on Saturday because of threats against them.
Denmark has also temporarily withdrawn diplomatic staff from embassies in Syria and Iran over security concerns.