National Security Advisor Gen. Jim Jones said this evening that Karzai did not ask for a suspension of U.S. air strikes while the investigation occurs but was "genuine" in his acceptance of Obama's condolences for the loss of innocent life there.
"It was clear that President Karzai was moved by that, by the president's statement, and he thanked the president for, for starting off the meeting with that -- that expression of condolence," Jones said.
Jawad explicitly said the United States was behind civilian casualties, and that more needs to be done to prevent such attacks.
"And any time civilians are killed, it's a tragedy. Everyone loses. The poor Afghan civilian getting killed is the prime victim but also the international community that's fighting terrorism in Afghanistan has the prime objective of keeping the civilians safe and on their side," he said. "So we are asking once again to come up with better measures to prevent any kind of death to the civilians, which are our most important ally in the war against terrorism in Afghanistan and in the region."
Karzai said that Afghanistan will work on its relationship with Pakistan, calling the two countries "conjoined twins" who share suffering, and said that his country will work to create a stronger partnership to work against extremism.
His counterpart, Zardari, echoed the same tone. He assured Americans and Afghans that "we will also be far more transparent in our actions," not explaining what that transparency would entail.
"This is a cancer," he said. "It needs to be done away with. Pakistan carries a huge burden, confronting al Qaeda and Taliban together, but we are up to the challenge, because we are the democracy, and democracy is the only cure to this challenge."
White House officials said going into the meetings that Obama will push Karzai and Zardari to commit to work more intensely and cooperatively to fight al Qaeda and other extremists.
"The core principle of this meeting is the centrality of Pakistan and Afghanistan to our own national security," a senior administration official said. "We face a common threat."
Obama held separate meetings with both Karzai and Zardari, and then met with both leaders and their delegations together.
In the evening, Vice President Joe Biden will host a dinner with Karzai and Zardari, their respective delegations and congressional leaders.
After Pakistan attempted to enter into a deal with Taliban leaders in April, ceding them the Swat Valley, the Obama administration expressed growing concerns about the stability of Pakistan, a nation with nuclear weapons.
Obama was asked at his news conference last week if he could reassure the American people that Pakistan's nuclear arsenal is secure, even with ongoing fighting with the Taliban there.
"I'm confident that we can make sure that Pakistan's nuclear arsenal is secure," he said. "Primarily, initially, because the Pakistani army, I think, recognizes the hazards of those weapons falling into the wrong hands. We've got strong military-to-military consultation and cooperation."
But Obama said last week he is "gravely concerned" about the "very fragile" civilian government in Pakistan.
Adm. Michael Mullen, chairman of the Joint Chiefs of Staff, said Monday he remains "comfortable" that Pakistan's nuclear weapons are secure and does not think those weapons could get into the hands of terrorists.