Karzai listed a number of foreign groups that he says are sending fighters to his country: "Name them al Qaeda, name them Islamic Movement of Uzbekistan, name them Haqqani, name them Taliban, whatever. They're still there. And they have the ability to continue 10 years on to come and hurt us and kill your troops and kill our troops, kill our civilians. We must then question how come they've returned?"
Karzai told Logan, "Something must have gone wrong" for the foreign troops to have returned.
Gen. John Allen, the top U.S. commander in Afghanistan, agreed with Karzai that "al Qaeda has come back." But Allen told "60 Minutes" that al Qaeda is "not here in large numbers. But al Qaeda doesn't have to be anywhere in large numbers."
"Al Qaeda has significance beyond its numbers, frankly," Allen continued. "And so for us, our 24-hour-a-day objective is to seek out those al Qaeda cells. And, as we seek them out, to target them and eliminate them. And we're doing that 24 hours a day. We do not want al Qaeda to feel as though it can put down roots here. That's the key."
Karzai said he disagrees with Gen. Allen, who has told him that security is much better in Afghanistan -- and it's the government that needs to improve.
"The security situation isn't perfect around the country," Gen. Allen said. "But an awful lot of the population of this country is living in an area where there is vastly improved security from where it was just a few years ago."
Allen agreed that enemy safe havens inside Pakistan are a major problem for the U.S.
"I'm not going to be able to wage war in Pakistan. But this is hard," he said. Gen. Allen said he will "do everything we can to hunt down and kill" every one of the foreign fighters who "come out of those safe havens" to kill U.S. troops in Afghanistan.
Allen told Logan that with 27 months to go until the majority of U.S. troops are pulled out of Afghanistan, he expects the fighting to last until the final day.
President Obama does not discuss the war in Afghanistan on the campaign trail, but on Sept. 18, his spokesman Jay Carney said the military "continues to work to understand why there has been a spike" in insider attacks.
"And we're working with Afghanistan to take measures to better protect our troops."
Carney said Obama's "policy of gradually turning over security lead to Afghan forces continues," and will result in "more American troops coming home and Afghans taking more and greater responsibility for the security of their nation."
The increasing number of insider attacks won't affect the 2014 withdrawal deadline that President Obama has set for U.S. troops, Carney said.