He says he first eluded an assassin in 2006, and bombers had targeted him 3 times since, before Thursday's attack.
Karzai, in his interview, also said that he was not convinced that al-Qaida "has a presence in Afghanistan."
While weakened in recent years, the group, whose 9/11 attacks drew America into its longest war, appears to have preserved at least limited means of regenerating inside Afghanistan as U.S. influence in the country wanes. For years the main target of U.S.-led forces has been the Taliban, who ruled Afghanistan and protected al-Qaida before the U.S. invasion 11 years ago. But the strategic goal is to prevent al-Qaida from again finding sanctuary in Afghanistan from which to launch attacks on the U.S.
"I don't even know if al-Qaida exists as an organization as it is being spoken about," Karzai said. "So all we know is that we have insecurity."
In other developments, five children were killed and two others were wounded Thursday in Sangin district of Helmand province, said provincial police spokesman Fareed Ahmad. He said the children had been collecting scrap items they hoped to sell and apparently picked up a mine. The mine exploded near shops in the district, he said.
Also on Thursday, Afghan and Tajik counter-narcotics officials said a dozen suspected drug traffickers were arrested during a joint operation along the border between the two countries.
Baz Mohammad Ahmadi, Afghanistan's deputy interior minister for counter-narcotics, said Thursday that alleged ringleaders of four drug-trafficking operations in Badakhshan in northeastern Afghanistan and nearby areas of Tajikistan were among those arrested.
Weapons and 420 kilograms (926 pounds) of hashish, opium and heroin also were confiscated, he said. Two of the alleged traffickers were wounded in gun battles during the five-day operation.
U.S. drug officials and the NATO-led coalition lent technical support for the operation that began Dec. 1.
Ahmadi said the Afghan government plans to burn 200 metric tons (220 short tons) of drugs seized in operations this year.
Insurgents conduct targeted attacks to undermine public confidence in the government and show they remain a resilient force, despite being outmanned by Afghan and U.S.-led coalition forces.
Associated Press Deb Riechmann, Heidi Vogt and Patrick Quinn contributed to this report.