They canceled the trip after Iran's ambassador to Denmark asked the group to condemn the publication earlier in the week of a cartoon lampooning the prophet.
"They can't and they won't," spokeswoman Mette Vestergaard said.
On Wednesday, more than a dozen Danish newspapers reprinted a cartoon that had sparked massive protests in Muslim countries two years ago. The newspapers published the caricature in an act of solidarity after police revealed an alleged plot to kill the cartoonist.
The lawmakers had planned to meet with members of Iran's parliament and to look into issues such as human rights and uranium enrichment.