"It is the government's clear commitment to relieve the pressure on Europe's external frontiers, at the same time making life as hard as possible for traffickers," Inger Støjberg told Danish daily Berlingske.
The anti-migration Danish People's Party, which Støjberg represents, voiced full support for the solution.
"I believe that Denmark as a country must join in this here and see whether can coordinate the effort to get it through the EU," Danish People's Party spokesman Martin Henriksen told Berlingske.
At the same time, the two countries have modest refugee support and maintain harsh penalties for violent crime, which makes them a less desired destination for Arabs fleeing Iraq or Syria than the famously lenient EU nations.
The idea is that Western support will dissuade potential customers from using human smugglers in search of a more comfortable life.
At present, the Mediterranean Sea remains an extremely popular refugee route, even if the current has subsided compared with last year's peak figures.
However, the stream of asylum-seekers may bounce back, as Turkish President Recep Tayyip Erdogan in late November threatened to re-open the Turkish border with the European Union for Syrian refugees as a counterpunch to the European Parliament's decision to freeze EU membership negotiations with Turkey.
At present, it is almost impossible to predict how many of the roughly 3 million Syrian refugees would begin their trek westwards if Erdogan carried out his threat to "open the gates." One of the reasons why last year's flow of refugees dried up is that the so-called Balkan route was closed though re-introduction of border controls. In Greece alone, there are tens of thousands of refugees who cannot get anywhere.