BRUSSELS  After months of anguished debate in the United States over how many new troops to send to Afghanistan, the numbers game switched to Europe on Friday, with NATO announcing that it planned to commit an additional 7,000 soldiers to the coalition in Afghanistan.

NATO portrayed the pledge as a powerful vote of support for the American-led effort. But in Europe as in Washington, arithmetic on troops can get fuzzy. Of the 7,000 troops promised by NATO, from 1,500 to 2,000 are already in Afghanistan, sent months ago to bolster security during the presidential election.

An undisclosed number of the new troops will steer clear of the fighting because they are barred by their countries from combat operations. And two allies, the Netherlands and Canada, still plan to withdraw nearly 5,000 troops in the next two years, offsetting the infusion.

NATO’s secretary general, Anders Fogh Rasmussen, declined to specify which countries would be sending troops, or when. Nor did Germany and France seem to budge from their reluctance to commit any more soldiers.