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“I think … it’s appropriate to talk about getting the job done,” he said. “I think it’s also appropriate to talk about the commencement of transition … while even beyond that, discussing the initiation of discussions on a strategic partnership with our Afghan partner.”

Defense Secretary Robert M. Gates said last week while visiting Kabul that a U.S. delegation would begin discussions this week with the Afghan government on sketching out a relationship that would last beyond 2014, the target date for ending U.S. and NATO combat. In her testimony Tuesday, Ms. Flournoy offered no details but said the U.S. interest lies in providing longer-term training to Afghan forces.

“We are in the process of discussing what kind of parameters should outline that partnership,” she said. “I should also add, it goes far beyond the military domain, to look at how we can support further development of governance, economic development and so forth.”

She said this would not involve any permanent U.S. military bases in Afghanistan.

Gen. Petraeus said much of the Taliban’s battlefield momentum has been halted, putting the U.S. on course to begin pulling out troops in July and shifting security responsibility to the Afghans.

“The momentum achieved by the Taliban in Afghanistan since 2005 has been arrested in much of the country and reversed in a number of important areas,” Gen. Petraeus said. “However, while the security progress achieved over the past year is significant, it is also fragile and reversible.”

Pressed repeatedly by lawmakers as to why U.S. forces should stay in Afghanistan, Gen. Petraeus said, “Two words, and those are 9/11,” referring to the Sept. 11, 2001, terrorist attacks. He said the United States made a grievous error in abandoning Afghanistan once before.

“I think it would be a mistake, a big mistake, to go down that road again,” he said.