Obama, who telephoned Karzai last night, "extended his condolences to the people of Afghanistan, and made clear his administration`s commitment to establish the facts as quickly as possible and to hold fully accountable anyone responsible," the White House said in a statement.
Obama called Karzai to express his "shock and sadness" over the killing of 16 civilians, mostly women and children. He "reaffirmed our deep respect for the Afghan people and the bonds between our two countries," the statement said.
Before speaking to Karzai, Obama had issued a statement describing the Kandahar incident as "tragic and shocking", which did not represent American values. "This incident is tragic and shocking, and does not represent the exceptional character of our military and the respect that the US has for people of Afghanistan," he said.
"I am deeply saddened by the reported killing and wounding of Afghan civilians. I offer my condolences to the families and loved ones of those who lost their lives, and to the people of Afghanistan, who have endured too much violence and suffering," Obama said.
US-Afghan ties had plunged to an all-time low last month after the burning of copies of Quran at the American-run military base in Bagram, an incident which triggered anti-US protests across Afghanistan which left around 40 people dead.
US Defence Secretary Leon Panetta also called Afghan President Karzai to express his condolences. "A suspect is in custody, and I gave President Karzai my assurances that we will bring those responsible to justice. We will spare no effort in getting the facts as quickly as possible, and we will hold any perpetrator who is responsible for this violence fully accountable under the law," Panetta said. A full investigation is already underway, he added.
Shocked and saddened that a US service member was alleged to be involved in the incident, Panetta said he told Karzai that the American people shared the outrage felt by him and the Afghans. "This tragic incident does not reflect the commitment of the US military to protect the Afghan people and help build a strong and stable Afghanistan," he said.
"As we mourn today with the Afghan people, we are steadfast in our resolve to work hand in hand with our Afghan partners to accomplish the missions and goals on which we have been working together for so long," Panetta said.
"This terrible incident does not reflect our shared values or the progress we have made together. As I told President Karzai, I am fully committed to ensuring that our cooperation continues. It is essential to forging a more peaceful future for the citizens of both our nations."
Gen Martin Dempsey, Chairman of the US Joint Chiefs of Staff, has been receiving regular updates following the incident, his spokesman said. He has been in contact with the International Security Assistant Force Commander and is confident that Gen John Allen, Commander of US and NATO forces in Afghanistan, and his staff are taking the appropriate steps to quickly and thoroughly investigate the circumstances of the incident.
Obama, in his statement, said he "fully supports Secretary Panetta`s and General Allen`s commitment to get the facts as quickly as possible and to hold accountable anyone responsible."
In a statement issued by the Pentagon, Gen Allen said: "I pledge to all the noble people of Afghanistan my commitment to a rapid and thorough investigation."
He said he was "shocked and saddened" by the incident in which a US soldier walked out of his base in the southern Kandahar province and opened fire on men, women and children.
He said ISAF would continue to offer medical care for those who were injured in this shooting. "We will maintain custody of the US service member alleged to have perpetrated this attack. And we will cooperate fully with local Afghan authorities as we ascertain all the facts," Allen said.
"This deeply appalling incident in no way represents the values of ISAF and coalition troops or the abiding respect we feel for the Afghan people. Nor does it impugn or diminish the spirit of cooperation and partnership we have worked so hard to foster with the Afghan National Security Forces," he said.
Meanwhile, Taliban in Afghanistan pledged revenge against Americans for the killing of 16 civilians in Kandahar. The Taliban would "take revenge from the invaders and the savage murderers for every single martyr", they said in a statement.