Opposition is growing in Denmark to plans by the ruling rightwing coalition to deny citizenship to any immigrant who declines to shake hands with their local mayor during a revamped naturalisation ceremony – a measure widely seen as targeting Muslims.

An opinion poll published on Thursday showed 52% of respondents opposed the proposal, part of tough new rules for obtaining Danish citizenship introduced by the minority conservative government in June. Several mayors have said they will ignore the requirement if the law is passed.

“It’s absurd that the immigration minister thinks this is an important thing to spend time on,” said Kasper Ejsing Olesen, the mayor of the central town of Kerteminde. “Shaking hands does not show if you are integrated or not. I think I will probably find an excuse and the deputy mayor will come to work that day.”

Another mayor, Ole Bjørstorp of Ishøj, said the demand was unreasonable and unconstitutional. “I’m obliged to take into consideration the fact that we have freedom of religion in Denmark. That’s the decisive factor for me,” he said.

The proposal to include a mandatory handshake in the new citizenship ceremony was tabled by the Conservatives, a member of the three-party coalition, and the far-right Danish People’s party (DPP), on whose parliamentary support the minority government depends.

It has the backing of several prominent government figures. “A handshake is how we greet each other in Denmark,” the hardline immigration minister, Inger Støjberg, of the Venstre party, the senior coalition partner, said this month. “It’s the way we show respect for each other in this country.”

Some Muslims do not shake hands for religious reasons, preferring instead to place a hand on their chest in a gesture of polite greeting. The practice has caused problems in several countries including Denmark, where in 2015 a taxi driver won DKK10,000 (now about £1,200) in compensation after being sacked for refusing to shake his female employer’s hand.

In Switzerland last month, a Muslim couple were denied citizenship because they refused to shake hands with members of the opposite sex at interviews. In Sweden a woman was awarded SEK40,000 (£3,400) after her job interview was cut short when she refused to shake hands with a male interviewer. France’s top court ruled this year that an Algerian woman’s refusal to shake hands with male officials at a naturalisation ceremony was reason enough to deny her citizenship.

Denmark’s immigration and integration policies have shifted significantly to the right in recent years, accompanied by a rise in anti-Islam rhetoric from even the left-leaning Social Democrats, who have called the religion a barrier to integration and said some Muslims did not respect Denmark’s judicial system and some Muslim women were choosing not to work for religious reasons.

In June, MPs passed a law that in effect banned the full-face veil. The government is also pushing through strict cultural assimilation laws including measures forcing immigrants to put their children into daycare for 25 hours a week from the age of one; setting quotas on nurseries so no more than 30% of children come from immigrant backgrounds; and doubling the sentences for crimes committed in designated “ghetto” areas.

Parliament has broadly backed the new citizenship bill, which introduces a naturalisation ceremony at which applicants must sign a document pledging to uphold the constitution, commit to core Danish values and “act respectfully towards representatives of the authorities” – which the conservative parties insist means shaking hands.

The DPP’s immigration spokesman, Martin Henriksen, said a handshake amounted to “a compromise about acting with respect. That, in our view, certainly means shaking the hand of the mayor or other person conducting the ceremony.” He said he expected parliament to back the proposal.

The Conservative party spokesman, Naser Khader, said this month: “The package includes a ceremony at which you make a statement of loyalty and shake hands.” He said he did not expect problems. “Some people would give their right arm for citizenship. I’m sure they’d also give their hand.”

The Social Democrats have said they believe a handshake is important and “completely natural”, but the party’s leader, Mette Frederiksen, has expressed doubts about the need to make it mandatory.

“We make too many laws in Denmark,” she told the state broadcaster DR. “The ceremony is what’s important to me. If there turns out to be problems with the handshake, we should discuss legislating then.”