The move comes in response to a request from NATO commanders who say they need as many as 3,000 additional troops from the allies. That number does not include an expected contribution of roughly 4,000 American forces.
They would be divided between the NATO training and advising the mission in Afghanistan, and America's counterterrorism operations against the Taliban, al-Qaida and Islamic State militants.
NATO Secretary-General Jens Stoltenberg said the NATO defense ministers' meeting in Brussels on Thursday that 15 countries "have already pledged additional contributions." He expected more commitments to come.
"We're in it for the long haul. It's a democracy. It's asked for our help and it's important that Europe responds," British Defense Secretary Michael Fallon told reporters.
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"Transnational terror groups operate in Afghanistan, are a threat to us in Western Europe."
European nations and Canada have been waiting to hear what US Defense Secretary Jim Mattis will offer or seek from them. US leaders have so far refused to publicly discuss troop numbers before completing a broader, updated war strategy.
Marine Gen. Joseph Dunford, chairman of the US Joint Chiefs of Staff, was in Afghanistan this week, meeting with commanders to gather details on what specific military capabilities they need to end what American officials say is a stalemate against the resurgent Taliban.