The “Af-Pak’’ strategy is based on the false premise that Pakistan and the United States are both opposed to Islamist influence in Afghanistan. In reality, Pakistan has long supported the Taliban insurgents there for what it considers a compelling strategic reason: to counter the influence of India in Kabul.

Despite this, the United States continues to give military aid and $800 million in annual cash subsidies to the Pakistan Army, supposedly for the express purpose of fighting the Taliban.

Until this pretense is ended, the United States will remain mired in a stalemate with Pakistan-supplied Taliban fighters. Equally important, Islamabad will be increasingly emboldened to demand the exclusion of Indian influence from Afghanistan as the price for cooperation there. Given India’s strong opposition to Islamist forces, this would directly conflict with US interests and goals.

Defenders of aid to Pakistan argue that its Inter-Services Intelligence directorate, the ISI, has given the CIA valuable information about Al Qaeda. Another compelling reason for US reluctance to threaten a cutoff of subsidies and aid is that Islamabad could counter by denying transit through Pakistan to supply US forces in Afghanistan.

“With one hand, they threaten to prevent you from prosecuting the war unless you pay them off,’’ Said Jawad, the Afghan ambassador to the United States, said. “With the other, they help the Taliban to make sure that the war keeps going on and the aid keeps flowing.’’

To escape from this trap, the United States should make three policy changes:

First, the administration should make clear that it recognizes the right of India, as the preeminent South Asian power, to be a major player in Kabul. The spokesman of the Pakistan armed forces, Major General Athar Abbas, criticizing the “overinvolvement of Indians in Afghanistan’’ in a July CNN interview, specifically warned against any Indian role in training the Afghan Army. But such a role could be a valuable supplement to the current faltering US-NATO training efforts. Indian aid to Kabul has so far been limited to $1.2 billion in economic aid.

Second, the Obama administration should seek Pakistan’s help in negotiating peace agreements with local Taliban factions, following up earlier Saudi Arabian initiatives. To get Taliban participation, such agreements would have to include a timetable for phased withdrawal of most US forces from all but the major cities and highways of Afghanistan.

Third, local peace agreements should be linked to a larger peace process negotiated at regional conferences attended by India, Iran, Russia, and China, in addition to the United States, NATO, Pakistan, and Saudi Arabia.

India feels encircled by ISI-supported Islamist forces operating out of Bangladesh and Nepal as well as Afghanistan and Pakistan. Shi’ite-majority Iran opposes the Sunni Taliban, and China, facing an Islamist uprising in Sinkiang, is increasingly wary of Taliban rule in Kabul. Bringing these nations into Afghan affairs would offset Pakistani support for the Taliban so that its influence remains confined to its strongholds in the ethnically Pashtun south and east and it does not become dominant in Kabul.

A peace process that leads to a phased withdrawal of most US forces would end the dependence of the United States on Pakistani supply lines. It would then be possible, at last, for the United States to use its enormous aid leverage in Islamabad effectively.

If the Al Qaeda leadership is still in Pakistan, and if ISI provides actionable intelligence that facilitates its destruction, then the existing US payoffs to the army should continue. But if Al Qaeda is no longer centered in Pakistan, as some suspect, or if ISI is unable to provide actionable intelligence, then the United States should restrict its aid to Islamabad to large-scale economic assistance focused on development and education. Maintaining friendly ties with Pakistan as a major Third World country and a nuclear weapons state should continue to be a US priority. But the tail should no longer wag the dog.

Selig S. Harrison, author of “Out of Afghanistan’’ and “In Afghanistan’s Shadow,’’ is director of the Asia Program at the Center for International Policy.