His comments come after Hillary Clinton, the US secretary of state, said she was confident allies would support calls by Washington for more troops in Afghanistan.
Barack Obama, the US president, had called on other countries to come up with 5,000 to 7,000 troops to bolster an additional 30,000 forces from the US.
Hillary Clinton, the US secretary of state, is spending Friday explaining US plans to step up the campaign against the Taliban.
"This is the time for all of the international community to make sure it steps up to support the efforts of governance in Afghanistan and Pakistan to ensure stability in that crucial part of the world"
David Miliband, British foreign secretary
"There's an understanding about the importance of the mission that the president has described," she said before arriving at Friday's meeting, adding that the "response has been positive".
Rasmussen said the coming year will bring "new momentum" to the Afghanistan mission, he said during a talk with Nato foreign ministers in Brussels.
There are currently around 100,000 troops from 43 countries involved in the US-led operation in Afghanistan.
David Miliband, the British foreign secretary - whose country has so far committed an additional 500 troops - said alliance members must "ask themselves whether they are doing the maximum possible".
"We know the stakes are very high indeed. So this is the time for all of the international community to make sure it steps up to support the efforts of governance in Afghanistan and Pakistan to ensure stability in that crucial part of the world."
Italy's government has approved sending 1,000 extra soldiers to Afghanistan next year, the defence and foreign ministers announced on Thursday.
In addition to Italy, Britain, Georgia, Poland and Slovakia have all promised increased troop deployments, while key allies France and Germany appear to be leaning more toward providing trainers for Afghan forces.
But the Netherlands and Canada plan to withdraw their respective combat forces of 2,100 and 2,800 over the next two years, reflecting public unease with the war.
The US now has 71,000 troops in Afghanistan, while other Nato members and allies collectively have 38,000 service members there.
With the added reinforcements, the international forces will swell to more than 140,000 soldiers.
Clinton said the United States was seeking a range of help, including civilian assistance and military training, in order to prepare Afghanistan to take charge of its own destiny.
"We've got to bring the Afghan security forces into the fight," she said.