It considers Mr. Haqqani and his control of large areas of Afghan territory vital to Pakistan in the jostling for influence that will pit Pakistan, India, Russia, China and Iran against one another in the post-American Afghan arena, the Pakistani officials said.

Image Jalaluddin Haqqani, a senior fighter, is the father Siraj Haqqani, a Taliban commander. Credit... Ministry of Defense, via Associated Press

Pakistan is particularly eager to counter the growing influence of its archenemy, India, which is pouring $1.2 billion in aid into Afghanistan. “If America walks away, Pakistan is very worried that it will have India on its eastern border and India on its western border in Afghanistan,” said Tariq Fatemi, a former Pakistani ambassador to the United States who is pro-American in his views.

For that reason, Mr. Fatemi said, the Pakistani Army is “very reluctant” to jettison Mr. Haqqani, Pakistan’s strong card in Afghanistan. Moreover, the Pakistanis do not want to alienate Mr. Haqqani because they consider him an important player in reconciliation efforts that they would like to see get under way in Afghanistan immediately, the officials said.

Because Mr. Haqqani shelters Qaeda leaders and operatives in North Waziristan, Washington is opposed to including Mr. Haqqani among the possible reconcilable Taliban, at least for the moment, a Western diplomat said.

In his reply to the Americans, General Kayani stressed a short-term argument, according to two Pakistani officials familiar with the response.

Pakistan currently has its hands full fighting the Pakistani Taliban in South Waziristan and other places, and it is beyond its capacity to open another front against the Afghan Taliban, the officials said of General Kayani’s response. The offensive has had the secondary effect of constraining the Haqqani network in North Waziristan and driving some of its commanders and fighters across the border to Afghanistan, senior American military officials in Afghanistan said.

But implicit in General Kayani’s reply was the fact that the homegrown Pakistani Taliban represent the real threat to Pakistan. General Kayani argued that they are the ones carrying out attacks against security installations and civilian markets in Pakistan’s cities and must be the army’s top priority, the officials said.