In his Afghanistan speech last week, President Obama said we must “address terrorist safe havens in Pakistan.” He vowed to “press Pakistan to expand its participation in securing a more peaceful future,” “work with the Pakistani government to root out the cancer of violent extremism” and “insist that it keep its commitments.”

Missing from the president’s remarks was a strategy on how to induce a Pakistani break with Islamic militants. For the past decade, this shortcoming has hamstrung our efforts in Afghanistan and in the broader struggle against extremism and terrorism.

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Even with Osama bin Laden dead, the nexus between the Pakistani state and a syndicate of Islamic extremists remains a threat. Pakistan’s military continues to support the Taliban, the Haqqani network and Hizb-e-Islami against coalition and Afghan forces. The number of Pakistani operatives fighting for the Taliban and other insurgents has increased over the past year, senior Afghan officials say.

Pakistan has not been forthcoming about its motives, but several are plausible. It could be defensively hedging against a strong Afghan government that is close to India, Pakistan’s regional adversary. Islamabad might be concerned that Afghanistan could reduce cross-border water flows by building dams on the Kunar River and attempt to press for concessions on territorial disputes, or that India and Afghanistan might use Afghan territory to support Pakistani groups hostile to the government.

In sustaining the extremist threat, Pakistan may see a way to keep the United States engaged in the region and, therefore, financially supportive of its military and civilian government.

Alternatively, Islamabad could view installing a subordinate regime in Kabul as a first step in an ambitious plan to consolidate regional hegemony in Central Asia. When the city of Herat fell to the Taliban in 1996, the Pakistani former intelligence official Sultan Amir Tarrar — better known as Col. Imam — was helping Taliban forces. He reportedly messaged headquarters: “Today Herat, tomorrow Tashkent.”

The U.S. approach since Sept. 11 has not obliged Pakistan to clarify its intentions. Islamabad continues to deny that it is even aiding insurgents. So having a frank discussion — one that might lead to pragmatic, mutual accommodation — has been impossible. As we draw down our forces in Afghanistan, persuading the Pakistani military to abandon its strategy of supporting extremism and backing Afghan insurgents will become more critical and more difficult. Without Pakistan’s cooperation, the insurgency will continue, but in light of our announced departure, Islamabad will see even less reason to stop sponsoring proxies as it prepares for the post-U.S. struggle in Afghanistan.

Yet a destabilizing outcome is not inevitable. Washington has considerable leverage that it has not used to optimal effect. Pakistan relies on the United States and international organizations to remain solvent; its economy would be on the ropes but for a two-year $7.6 billion International Monetary Fund loan package. Coalition support funds from the United States alone are equal to about 25 percent of Pakistan’s defense budget.