The ministry said Monday that the first attack occurred before dawn in Baghlan province, north of Kabul, when a group of armed militants attacked a police checkpoint and killed eight policemen.
About the same time, militants attacked another police checkpoint in Lashkar Gah, the capital of Helmand province in southern Afghanistan. Another eight police were killed.
Both incidents are under investigation.
The attacks come as the Pentagon's top military officer arrived for a visit to Afghanistan on Monday, just as the first of the 30,000 U.S. reinforcements are starting to deploy to the 8-year-old war.
in the Afghan capital of Kabul for a series of meetings with the government of President Hamid Karzai, a spokesman for the international coalition force said.
President Obama told "60 Minutes" correspondent Steve Kroft in an interview broadcast Sunday evening that the decision to send 30,000 more young Americans into harm's way in Afghanistan was "absolutely" the most difficult decision of his presidency to date.
He acknowledged the waning support for the ongoing war effort in the American public, and even among his fellow Democrats, but told Kroft, he believed it was, "the right thing to do. And that's my job. If I was worried about what polled well, there are a whole bunch of things we wouldn't have done this year."
President Obama on "60 Minutes":
Obama Defends Afghanistan Timetable
Transcript: President Obama, Part 1
Transcript: President Obama, Part 2
Obama Versus the "Fat Cats"
Obama: Gatecrashers Lapse "Won't Happen Again"
Obama: Senate Will Pass Health Bill by Christmas