The party's foreign policy spokesperson, Søren Espersen, says that Danes of Turkish extraction must make a choice between the two countries.
Danish citizens cannot be servants to two countries, says the MP.
“Turkish people are mentally hanging on to a reality other than the one they are part of. If you live here with Danish citizenship, you are part of a Danish reality,” Espersen told newspaper Politiken.
Espersen's comments come in the wake of a diplomatic crisis between Turkey and a number of other European countries.
Turkish president Recep Tayyip Erdogan called Germany and the Netherlands “Nazis” and “fascists” last week after the two countries blocked Ankara politicians from rallying events aimed at foreign-based Turkish citizens eligible to vote in an upcoming Turkish referendum.
Espersen has previously said that foreign-based Danes, who would also be affected by a reversal of a 2015 law change allowing dual citizenship in Denmark, should be allowed to vote in domestic elections.
“When you have a Danish passport in your hand, Danish citizenship and the right to move back to the country, then I think it is fair to be allowed to vote,” Espersen told broadcaster DR in 2015.
Danish law currently states that people registered as living abroad may not vote in elections at home.
“I was affected by this myself when I lived in Great Britain. I could neither vote in British nor Danish elections,” Espersen told Politiken.
The MP said that the argument for allowing foreign-based Danes to vote is a different one to the discussion of the Turkish voters with dual citizenships.
“Many live in Sweden now and cannot vote. But they only have one citizenship. The introduction of dual citizenship has created a big mess and it is only going to get worse,” he said.
Earlier this week, Norway's governing Høyre (Conservative) Party voted in favour of allowing dual citizenship in Denmark's northern neighbour - the only Nordic country that currently does not allow double nationality.
Espersen told Politiken that he thinks Danish-Turkish citizens should give up their Turkish citizenship.