"It is a very unfortunate situation," Lars Løkke Rasmussen told the Ritzau news agency after briefing leaders of Denmark’s political parties on his government’s response.
"We have spent billions on building infrastructure up in the Öresund region," he said. "We have spent millions branding Copenhagen and Malmö as a single metropolitan area."
Sweden last week announced that it intended its tough new border regime at the famous Öresund bridge linking the two countries to come into effect on January 4th.
The plans are expected to be approved by parliament on Thursday.
As part of the regime, Sweden is compelling all companies whose trains or ferries cross Sweden's borders to ensure that their passengers are carrying valid ID documents beforehand.
Løkke Rasmussen said that his government had on Monday informed Denmark's other parties in that the country was prepared to impose temporary border controls at its own borders with Germany, if the Swedish move led to a marked growth in asylum applications.
But he stressed that Denmark's authorities would only take such extreme measures if there was evidence that it would reduce the numbers seeking asylum in the country.
"We do not want to take on a Swedish immigration policy," he said.
"It is our clear opinion, after analyzing the situtation that if we established a border in Denmark today, we would get more, not fewer asylum seekers."
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Sweden has seen a nationwide dip in the number of people claiming asylum in recent weeks, following news of the tighter border checks and a government announcement that it would cut the number of residency permits made available.
While in October around 10,000 people were registered in a week, Migrationsverket statistics suggest that 4,721 people sought asylum across Sweden during the first seven days of December.
Meanwhile, Denmark had received roughly 18,000 between January and November.