Panetta told a Pentagon news conference that the U.S. should have an "enduring presence" in Afghanistan to pursue the counterterrorism effort, and to train and advise Afghan forces.
Panetta said al-Qaida poses a continuing challenge in Afghanistan, even though it currently has only an estimated 100 fighters in the country and has suffered many setbacks since the U.S-led invasion in 2001.
"The fact is that they continue to show up," Panetta said, adding that intelligence indicates that they are looking for ways to strengthen their position and influence in Afghanistan.
Last week Panetta said al-Qaida and affiliated terrorist groups in Pakistan see the rugged reaches of northeastern Afghanistan—especially the provinces of Kunar and Nuristan—as a viable safe haven. He vowed not to permit them to regain that sanctuary.
In his remarks Thursday, Panetta would not say how many American troops he thinks will be needed to conduct the counterterrorism mission—nor did he mention a time period. He said the size of the counterterrorism force is now under discussion.
The U.S. currently has about 66,000 troops in Afghanistan. The Obama administration is considering how many should remain after 2014, with some officials favoring a figure of about 10,000.