Norwegian Foreign Minister Jonas Gahr Store also expressed concern.
"If the Iranian efforts to get nuclear weapons continue, I wouldn’t dare rule out tougher sanctions," Rasmussen told reporters at his weekly news conference.
Rasmussen said however a "military response" was not on the cards.
"There has been broad support to follow the diplomatic track in the (United Nations). For the time being that has been a successful strategy. And we wish to continue that. It is encouraging that the UN Security Council has showed decisiveness," Rasmussen said according to Danish news agency Ritzau.
The Danish premier also rejected suggestions that sanctions had not had an impact on Iran.
Norwegian Foreign Minister Jonas Gahr Store said he was "concerned" over Iran’s decision to continue its uranium enrichment program.
"These developments give grounds for concern, and will make finding a political solution to the nuclear dispute even more difficult," Store said in Oslo, adding that Iran can only regain its "international credibility" by suspending its enrichment programs.
Store added that "Norway supports the international demands made of Iran by a unanimous UN Security Council. Iran must now show real willingness to contribute to a negotiated solution."
Iran on Monday said it had begun an industrial scale uranium enrichment program at its Natanz plant in central Iran, but did not offer details.