President Barack Obama lauded Pakistan as a “strong counterterrorism partner” with the United States since Sept. 11 and framed the death of al-Qaida leader Osama bin Laden as an opportunity for the two nations to work better together in the future.

“There have been times where we’ve had disagreements,” the president said during an interview aired Sunday on CBS’ “60 Minutes.” “There have been times where we’ve wanted to push harder and for very various concerns they might have hesitated, and those differences are real. And they’ll continue. But the fact of the matter is we’ve been able to kill more terrorists on Pakistani soil than just about anyplace else. We could not have done that without Pakistani cooperation.

“And I think that this will be an important moment in which Pakistan and the United States gets together and says, all right, we’ve gotten bin Laden, but we’ve got more work to do and are there ways for us to work more effectively together than we have in the past, and that’s going to be important for our national security,” he said in the interview, which was his first broadcast since U.S. Navy SEALs killed bin Laden in Pakistan on May 1.

Senate Foreign Relations Chairman John Kerry (D-Mass.) and ranking member Dick Lugar (R-Ind.) were skeptical Sunday that Pakistan was unaware of bin Laden’s compound in Abbottabad, where Pakistan’s military academy is located. Other lawmakers have called on the United States to re-examine aid to Pakistan in light of the revelation.

U.S. officials believe that bin Laden had a support network in Pakistan, Obama said, but they are still trying to determine whether it extended to government or intelligence officials.

“We think that there had to be some sort of support network for bin Laden inside of Pakistan, but we don’t know who or what that support network was,” he said. “We don’t know whether there might have been some people inside of government, people outside of government, and that’s something that we have to investigate and, more importantly, the Pakistani government has to investigate.”

The Pakistani government has expressed “profound interest” in discovering more about the support networks, the president said. But he warned that answers won’t come immediately.

“But these are questions that we’re not going to be able to answer three or four days after the event,” he said. “It’s going to take some time for us to be able to exploit the intelligence that we were able to gather on site.”

Obama added that he hopes that the information the SEALs collected from the compound could lead U.S. officials to other terrorists, as well as reveal the inner workings of al-Qaida.

“We now have the opportunity — we’re not done yet — but we’ve got the opportunity, I think, to finally defeat at least al-Qaida in that border region between Pakistan and Afghanistan,” he said. “That doesn’t mean that we will defeat terrorism, it doesn’t mean that al-Qaida hasn’t metastasized to other parts of the world where we’ve got to address operatives there. But it does mean we’ve got a chance to, I think, really deliver a fatal blow to this organization if we follow through aggressively in the months to come.”

Obama credited some of the mission’s success to the boost in troops in Afghanistan to target the Taliban and al-Qaida.

“We’ve denigrated al-Qaida significantly even before we got bin Laden, and I think it’s important for everybody to understand that the work that’s been done in Afghanistan helped to prepare us for being able to take bin Laden out,” he said.

The United States is scheduled to begin drawing down troops from Afghanistan in July, and Obama stood by the timeline.

“It’s important to understand that our job’s not yet finished and that we’ve got to make sure that we leave an Afghanistan that can secure itself, that does not again become a safe haven for terrorist activity,” he said. “But I think that they can be accomplished on the timeline that I’ve already set out.”