Taliban leader Fakhtar Mohammad Mansour on Aug. 1, 2015. (Rahmat Gul/Associated Press)

THE OBAMA administration says the killing of Taliban leader Akhtar Mohammad Mansour in a U.S. drone strike “eliminates one roadblock to peace in Afghanistan,” as Defense Secretary Ash Carter put it in a statement. While that may be true — Mansour was said to have resisted negotiations with the Afghan government — the Taliban chief was not the only nor even the most important block to an Afghan settlement. Unless and until President Obama addresses some of the others, including his own reluctance to provide adequate support to the Afghan military, Saturday’s strike can’t be expected to much improve a deteriorating situation.

The Taliban head, who was formally named last summer, was said to have resisted pressure from Pakistan to take up the offer of peace talks pressed by Afghan President Ashraf Ghani. The airstrike that killed him occurred in Baluchistan, the Pakistani province that has long been the base of the Taliban’s leaders, and appeared to be the first U.S. drone attack in that area. While U.S. officials said Pakistan was not informed in advance, the relatively mild initial protests from Islamabad suggested some degree of acquiescence with the U.S. move.

Whether the killing will advance the dormant peace process or slow the Taliban’s ongoing military offensive is far from clear. The insurgents’ current military operations are said to be directed by Sirajuddin Haqqani, a Pakistani client and implacable U.S. enemy who could become the next Taliban head. If so, a settlement would look improbable. In any case, the Taliban’s annual offensive, which is pressing the government hard in both the south and east of the country, is unlikely to slow. Having regained substantial ground in the last year, and inflicted some 5,500 combat deaths on the Afghan army, the Taliban has little incentive to stop fighting and cut a deal.

That’s where the obstacles created by Mr. Obama come in. To his credit, the president decided last fall to set aside his ambition to withdraw almost all U.S. troops from Afghanistan by the end of his term, and allowed 9,800 to remain through most of this year. However, he has not yet revised a plan to reduce that number to 5,500 by early 2017, though several senior U.S. commanders have suggested publicly that any further withdrawal should be “conditions-based.”

Nor has Mr. Obama agreed to loosen the restrictions on U.S. airstrikes against Taliban forces, which are allowed only if U.S. troops are under attack or a government unit is in danger of collapse. The recently departed U.S. Afghanistan commander, Gen. John Campbell, proposed that Afghan forces receive U.S. air support until the government can build up its own air force. In a recent Wall Street Journal op-ed written with Michael O’Hanlon of the Brookings Institution, former commander David Petraeus pointed out that in the first three months of this year, U.S. and allied planes dropped 7,000 bombs in Iraq and Syria, but only 300 in Afghanistan.

Gen. John W. Nicholson Jr., the new commander in Afghanistan, is preparing a recommendation on troop and air deployments that is expected to be completed by next month. If Mr. Obama is serious about helping Afghanistan move toward peace, he will approve the general’s likely request for more airpower and an extended troop presence.