WASHINGTON — The Obama administration’s top lawyer at the Pentagon laid out a vision on Friday for the legal challenges that will arise when the war against Al Qaeda winds down, looking ahead to when the terrorist network has been so degraded that the military conflict — and the legal authorities attached to it — will come to an end.

When that point is reached, said Jeh C. Johnson, the Defense Department’s general counsel, the primary responsibility for mopping up scattered remnants of the group and unaffiliated terrorists will fall to United States law enforcement and intelligence agencies, and pressing questions will arise about what to do with any military detainees who are still being held without trial as wartime prisoners.

“I do believe that on the present course, there will come a tipping point — a tipping point at which so many of the leaders and operatives of Al Qaeda and its affiliates have been killed or captured and the group is no longer able to attempt or launch a strategic attack against the United States, such that Al Qaeda as we know it, the organization that our Congress authorized the military to pursue in 2001, has been effectively destroyed,” Mr. Johnson said, according to a transcript of his speech.

Mr. Johnson emphasized that he was not declaring the war to be over, and that he could not say that even the “beginning of the end” of the armed conflict against the network was yet at hand. He said affiliates of Al Qaeda, particularly in Yemen and North and West Africa, remained a threat.