But the ultimatum could force painful choices for thousands of Afghan troops, and it is likely to stoke ethnic tensions just as the country’s leadership is seeking a negotiated end to the war. Purging members of the military with family in Pakistan also has the potential to aggravate long-troubled relations between Afghanistan and its eastern neighbor. Afghan President Hamid Karzai visited Islamabad on Thursday in a bid to enlist Pakistan’s help in winding down the conflict.

The policy has not yet received final approval from the Defense Ministry, and Afghan officials are still weighing whether to apply it nationwide, even as implementation begins in some areas. Mere consideration of the policy reflects the depth of anxiety in Afghanistan — both among Afghan officials and Western powers — over sleeper agents within the military.

U.S. officials have expressed concern about the Taliban’s ability to penetrate Afghan security forces but have not publicly proposed concrete remedies. Afghan commanders say that the connection between sleeper agents and time spent in Pakistan has been well documented and that there is consensus on the need to act.

“When they’re in Pakistan, they can be influenced and intimidated by the enemy,” said Lt. Gen. Sher Mohammad Karimi, the army chief of staff. “It’s a big concern, and it’s something we’re trying to change.”

Insurgent groups such as the Taliban are widely believed to operate from bases in Pakistan, and militants frequently travel back and forth across the border. Pakistan has denied long-standing allegations that it provides insurgents with support.

Afghan counterintelligence officials have already compiled lists of soldiers with ties to Pakistan. In some parts of the country, such as the battle-scarred south, soldiers on the list have been told: Move or leave the army.

“We’ve told them, ‘If you can’t move your families, you’ll be kicked out,’ ” said Col. Abdul Shokor, the top Afghan counterintelligence official in the Afghan army’s Kandahar-based 205th Corps.

On his desk, Shokor keeps a list of several hundred soldiers based in southern Afghanistan who visit Pakistan during their time off from the military. No deadline has yet been set for the families to move, he said.

If the new rule is implemented nationally, it could affect several thousand soldiers. Millions of Afghan refugees fled to Pakistan in recent decades to escape the fighting. About 1.7 million Afghans still live there, according to the Office of the U.N. High Commissioner for Refugees. Afghan soldiers often leave their families in Pakistan for security reasons.