The coming year will bring "new momentum" to the Afghanistan mission, he said during a talk with Nato foreign ministers in Brussels.
Nato officials have said pledges have so far exceeded an additional 5,000 troops to the mission, but have warned that the total may fall short of US expectations.
More than 20 nations are expected to make firm commitments at a conference on Monday, Rasmussen said.
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.