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“We have made clear to Afghans and to the region that the security transition does not mean we are abandoning Afghanistan,” he said. “And the Taliban appears to be taking notice.”

The Taliban are “debating and signaling an openness to negotiations” with the Afghan government, but the militants must first renounce violence, cut ties with al Qaeda and accept the Afghan constitution, Mr. Cunningham said.

“I will not play down the difficulties,” he added, referring to efforts to build up Afghan security forces and fight political corruption.

However, he noted that Afghans have made “substantial gains” since the overthrow of the Taliban regime, which imposed a strict form of Islamic law that was especially brutal on women.

More than 8 million Afghan children, including more than 2 million girls, now are enrolled in schools. In 2001, Afghanistan had fewer than 1 million students and “nearly none of the girls,” Mr. Cunningham said.

“Ultimately,” he added, “the gains of the last decade must be sustained by the Afghan people themselves.”

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