Denmark has about 700 troops in the NATO force in Afghanistan.
Twenty-one have been killed since Denmark joined the US-led coalition in Afghanistan in 2002.
In the Netherlands, General Peter van Uhm said 24-year-old Sergeant Mark Weijdt was killed on Friday when he stepped on an explosive device during a fire-fight with the Taliban in the southern Afghan province of Uruzgan.
“It is terrible news that casts a dark shadow over Christmas,” Jan Peter Balkenende, the Dutch prime minister, said.
Weijdt’s death brings to 18 the number of Dutch troops killed in Afghanistan since August 2006, when the government took the unpopular step of sending 1,650 troops to serve with the NATO-led force.
Dutch troops are scheduled to leave Afghanistan in 2010. But Balkenende would not rule out extending the mission if US President-elect Barack Obama asks for help in the fight against the Taliban.