The US is calling on allies among the 43 nations with troops in Afghanistan to send about 10,000 extra soldiers.
Speaking at the Brussels talks, Mrs Clinton urged Nato and its partners to rally behind a new strategy to combat the insurgency and to "finish it together".
She said it was essential additional forces and non-military assistance be provided as quickly as possible.
"The need for additional forces is urgent, but their presence will not be indefinite," she told the meeting of Nato foreign ministers and representatives of non-Nato countries that have forces in Afghanistan.
Mr Rasmussen told delegates at Nato HQ that the coming year would "see a new momentum in this mission".
The BBC's Nick Childs, in Brussels, says the main thrust of Mr Rasmussen's speech was to insist on a message of solidarity, despite the challenges, and of unity behind the mission.
"In addition to the clear pledges already tabled, we have heard indications... that other allies and partners will probably be in a position to announce contributions in the coming weeks and months," Mr Rasmussen said.
"Isaf [International Security Assistance Force] will have at least 37,000 more soldiers in 2010 than it did this year.
"That is solidarity in action."
White House spokesman Robert Gibbs said the US was "extremely pleased" by Nato's promised contribution.
Warning for Kabul
But many Nato governments face publics even more sceptical about the mission than those of the US and Britain.
Italy has promised to send about 1,000 more troops to Afghanistan
Even if more public announcements are forthcoming, turning these into firm pledges of the right troops at the right time and for the right missions may take longer, our correspondent adds.
Mr Rasmussen said several countries had pledged additional funds for development assistance as part of the mission's new approach in providing basic services to benefit the local people in Afghanistan.
But he warned that Kabul had to play its part in the reconstruction process.
"None of these initiatives are of any use if it is not backed up by good governance, efficient governance in Afghanistan, including a determined fight against corruption, a determined fight against the drug trade," he said.
"So the international community stands ready to assist Afghanistan in promoting economic and social development but it also takes a strong effort from the Afghan people and not least the Afghan government."
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