Perhaps the most important consideration, administration and Congressional officials say, is whether the designation would make any difference in the group’s ability to raise money or stage more assaults as the American-led NATO force draws down in Afghanistan. Several Haqqani leaders have already been designated individually as “global terrorists,” so the issue now is what would be gained by designating the entire organization.

An administration official involved in the debate, who declined to speak on the record because of the continuing decision-making process, said, “The optics of designating look great, and the chest-thumping is an understandable expression of sentiment, but everyone has to calm down and say, ‘What does it actually do?’ ”

Mrs. Clinton, in the Cook Islands at the start of a trip to Asia, declined to discuss the internal debate but said she would meet the Congressional deadline in September. “I’d like to underscore that we are putting steady pressure on the Haqqanis,” she said. “That is part of what our military does every day.”

A National Security Council spokeswoman, Caitlin Hayden, would not comment on the administration’s internal deliberations, but hinted in an e-mail on Friday at the White House’s preferences for using other means to pressure the group. “We’ve taken steps to degrade the Haqqani Taliban network’s ability to carry out attacks, including drying up their resources, targeting them with our military and intelligence resources, and pressing Pakistan to take action,” the e-mail said.

Critics also contend that a designation by the Treasury Department or the United Nations, or under an existing executive order, could achieve the same result as adding the network to the much more prominent State Department list, with far fewer consequences.