"We don't want to take more refugees than we have already taken," Friis Arne Petersen said, RIA Novosti reported.
"The population doesn't want to take more refugees."
Petersen added that he sees the resolution of the migrant crisis in a "common European approach," but that "that will be a difficult, very difficult path," and "Europe is split on the migration question."
He also expressed disquiet about the agreement the EU reached with Turkey to stem migration to Europe, and the prospects of Turkey fulfilling the necessary criteria for EU membership.
The renewal of talks on Turkey's accession to the EU was one of the political concessions to Ankara in return for cracking down on illegal migration and people smuggling.
In November the EU promised to pay three billion euros ($3.3 bilion) in financial aid to pay for refugees in Turkey, and during further negotiations last week Ankara demanded at least an additional three billion euros.
"We need Turkey as a strategic partner and EU member on the condition, of course, that it can adhere to the Copenhagen criteria," Petersen said.
We have to make that happen, but how to do so is a big question."
Petersen also called on all Western countries to take joint responsibility for the migration crisis, and singled out the US for particular criticism.
"Obama promised to take 10,000 refugees, but still hasn’t taken them," he said, and added Britain, France, Spain, Italy and Poland to the list of countries that are reluctant to accept more refugees.
The law requires asylum seekers to hand over money and valuables to the authorities in exchange for state provisions while their asylum request is being processed.
Such measures may have contributed to relatively lower numbers of refugees and migrants seeking asylum in Denmark. In comparison to neighboring Sweden, which received around 163,000 asylum applications during 2015, Denmark received just 18,000.
