Mr. Karzai has also opposed the forceful eradication of poppy crops, something that did not appear to be sanctioned by the new NATO mandate. Mr. Karzai has argued that other measures, including crop substitution and public education programs, along with foreign aid that provides jobs, are the most effective ways of cutting opium production without the violence likely to be provoked by crop eradication.

But American commanders have concluded that gaining the upper hand in the fight against the resurgent Taliban will require depriving the insurgents of income from the drug trade, which the top American commander in Afghanistan, Gen. David D. McKiernan, estimated at a Washington briefing last week to be a minimum of $100 million.

Despite the misgivings among some NATO allies, the American push for a NATO mandate that includes attacks on drug networks fueling the insurgency has been backed by the Afghan government, which reiterated the sentiment at the Budapest meeting.

The need for more aggressive action against the drug lords has also been pressed by the United Nations drug agency. In its August report, authored by its executive director, Antonio Maria Costa of Italy, it noted the “inextricable link between drugs and conflict,” and without referring to or sanctioning military action, said that something needed to be done.

Beyond that, the American commanders have been supported by Britain, whose 8,000 troops in Afghanistan are second only in numbers, among NATO nations, to the 33,000 American troops. British support is particularly significant, since most of the British troops are concentrated in Helmand Province in the southwest, the heartland of the opium trade and one of the most intensive battlefields of the insurgency. United Nations figures estimate that Helmand alone accounts for more than 50 percent of the country’s opium production.

According to the recent United Nations survey, 98 percent of Afghanistan’s opium comes from seven provinces in the southwest, with no opium at all produced in half of the country’s 34 provinces. The bulk of the NATO troops operating in the southwest come from the United States, Britain, Canada and Denmark, and it is those nations that are likely to be most affected by the new NATO mandate.

Together with the United States, Britain and Canada have already taken the heaviest casualties among the NATO nations fighting the Taliban and Al Qaeda, with NATO troops who have died in the seven-year war now approaching 1,000, including more than 600 Americans.