Rabih Azad-Ahmad, chair of the Multicultural Association, said the row had become too confrontational.
“Now, we have to demonstrate that we are proud of being Danish and that we are supporting Danish values,” he said.
In an unexpected turn, the reaction to the attacks on Danish embassies could help promote integration in Denmark.
“I didn’t know there were so many Muslims in Denmark who are supporting Western values,” said Soren Espersen, an MP for the populist Danish People’s Party.
His comments mark a turnaround for the party, which has grown to be the country’s third largest on a political platform of nationalism and xenophobia.
They are also likely to have been welcomed by a group of Danish writers who warned two months ago that the harsh tone in the national debate about Muslims and integration was comparable to Nazi rhetoric against Jews.
“Politicians and the media have a tendency to see Muslims only as criminal, anti-social elements and as potential rapists,” the writers said in an open letter.
However, some of the strongest protests against the cartoons have come from imams who are part of the government’s integration think tank.
“We want the newspaper to promise that this will never happen again, or this will never stop,” said imam Ahmad Akkari of the Islamic Faith Society.
For the Danish integration minister, Rikke Hvilshoj, that stance is a wake-up call.
“It is very clear that we cannot trust the imams any longer if we want integration to succeed in Denmark,” Mrs Hvilshoj says.
The conflict is also politically explosive for Prime Minister Anders Fogh Rasmussen.
The international crisis is his first big test after more than four years in office.
Former spin doctor and political commentator Peter Mogensen warned that if the violence does not stop soon, Mr Rasmussen could lose his job.
“The prospects of further escalation, of terrorist attack against Danish property and beheadings of Danes on al-Jazeera would make the current situation look like a picnic,” Mr Mogensen said.
The opposition has also accused the prime minister is acting too late.
No more apologies
Nonetheless, Mr Rasmussen’s government and its diplomats are working around the clock to control the damage.
Fifteen Muslim countries, from Algeria to Pakistan, are boycotting Danish goods. So far, nearly 200 jobs have been lost in Denmark.
More jobs could be on the line if the boycotts continue, as Denmark’s exports to the Arab world are worth almost $2.6 billion (?1.5 billion) a year.
While most Danish Muslims are satisfied by the apology already issued by Jyllands-Posten, the newspaper that first published the cartoons, half of Danes still think that the paper could do more to appease the Arab world.
Editor-in-chief Carsten Juste remains firm. “We are sorry for any offence caused by the drawings, but we cannot apologise for freedom of expression,” he said.
Since 2003, Denmark has supported a broad range of democratic projects and initiatives across the Arab world.
It is unclear how many of those countries will care to listen any longer. So far, all trips by Danish staff connected to these projects have been put on hold.
For many Danes the past two weeks have been surreal.
Since the time when many Danes helped thousands of Jews to safety from German-occupied Denmark in World War II, the Scandinavian country has had a reputation for being peace-loving and harmless.
That might still be true. But the perception among millions of Muslims has changed. And that will take years to bring back to balance.