"The negotiations are moving forward. We've gone a little deeper into what NATO is demanding," Ahlin said to news agency TT.
"And I don't mean the letter from Anders Fogh Rasmussen, (NATO's secretary general) but the more specific demand from NATO, based on the deficiencies in the operation that they need help with."
Ahlin says that the two parties have the same idea of what NATO wants.
One focus of the negotiations has been political solutions for Libya when there is a ceasefire, and the responsibility has passed from NATO to the UN and international contact group.
"We've had a lot of discussions of what the Swedish support should look like at that point," said Ahlin.
The topics are aid, humanitarian support, building democracy, and a naval force to monitor the arms embargo.
The question of using eight Gripen aircraft, which has been a sore point in the discussions, is now opening up for the debate.
While the Social Democrats continue to demand that the aircraft not be used in the enforcement of Libya's no-fly zone, Urban Ahlin now opens a window for the possibility of other Swedish flight missions.
"I'm not excluding the possibility that one or some Gripen will stay on for recon missions," he said to TT.
Prime minister Fredrik Reinfeldt is also open to bringing down the number of Gripen aircraft in Libya, if the Swedish air operation changes its focus.
When it comes to Swedish troops overseas, there is a long tradition of wide political agreements, over party lines, and the goal is to present such an agreement in Riksdag on Wednesday.