NATO said Tuesday two of those killed Monday night were later identified as "known insurgents," but Karzai and the provincial chief of police, Abdul Hakim Hesaq Zoy, said they were all civilians.
Zoy said one of the victims was a 12-year-old boy.
Lt. Col. Todd Vician, a NATO spokesman in Kabul, said the four were found to be unarmed. He added the military concluded two of the men were insurgents based on information found in the military's bio-metric database.
NATO released a statement saying the car kept accelerating toward the military convoy despite attempts to flag the vehicle down by flashing lights and firing warning shots.
"Several rounds were fired in an attempt to disable the vehicle, and finally shots were fired into the vehicle itself," the statement said.
Karzai said in a statement he "condemns the shooting of civilians by international forces."
"This act goes against the commitment of the international forces in Afghanistan to protect the people and fight against terrorists," he said.
The U.N. has called for better protection of Afghan civilians after the death toll rose last year to its highest level since the 2001 fall of the Taliban regime. Some 2,412 civilians were killed in 2009 — a 14 percent increase over the 2,118 who died in 2008, according to a U.N. report released in January. Nearly 70 percent of civilian deaths last year, or 1,630, were caused by the insurgents, the report found.
Also Monday, gunmen stormed a mosque and killed the deputy mayor of Kandahar as he knelt for evening prayers in southern Afghanistan.
The attack highlights the challenges facing NATO forces as they try to push the Taliban out of southern Afghanistan.
Azizullah Yarmal, who was in his 50s, was shot through the head as he and dozens of others began their prayers, Zalmai Ayubi, spokesman for Kandahar province, said Tuesday. Mosques typically provide little security, making them vulnerable to insurgent death squads.
"This is the work of the enemies of Afghanistan," Ayubi told The Associated Press, saying the assailants managed to escape. "They don't want these honest people to serve the Afghan people and work in government institutions."
Kandahar is the largest city in southern Afghanistan and the birthplace of the Taliban, which still has considerable support there. A U.S.-led operation planned for this summer aims to clear Kandahar of Taliban fighters break the grip of warlords who have allowed the fighters to slip back in.
President Barack Obama has ordered 30,000 more troops into Afghanistan, in part to back up the Kandahar offensive. The operation will be a critical test of the Afghan war.
But the Taliban have launched increasingly deadly attacks ahead of the offensive. Since April 12, at least 20 civilians have been killed in Kandahar, including children. Aid workers also have been the target of attack.
The looming offensive and the ongoing crime and insecurity has rattled Kandahar's half million inhabitants, who are deeply skeptical of Western promises.
"Every day we hear an operation is going to start in Kandahar, and that is the main reason the Taliban have increased their attacks — to show their power," said Amonullah Jan, a 32-year-old taxi driver. "We live our lives in fear. When we leave our homes in the morning we don't have any hope that we will make it home to see our families again."
Ayubi said Yarmal's assassination was among a series of killings of government workers in southern Afghanistan aimed at undermining central authority by terrorizing competent individuals into leaving their posts.
Insurgents were believed to have been behind the murder last week of an elderly tribal leader in neighboring Helmand province's Gereshk district. Lal Mohammad Khan was also shot while praying in a mosque.
Ayubi said other officials who were cut down include the head of Kandahar's provincial department of information and culture, and a former police official who was killed despite having left his post three years earlier following threats from the Taliban.
The U.S. hopes a successful operation in Kandahar will help the country become stable enough for parliamentary elections to be held in September. The vote will be the first since a fraud-marred presidential ballot last year that prompted Western countries to threaten to withdraw support.
On Tuesday, Afghan election officials said they are committed to keeping those involved in the fraud out of the upcoming vote. The election commission has asked the Attorney General's Office to investigate top electoral officials in four provinces that had some of the most flagrant violations — Kandahar, Paktika, Nangarhar and Ghazni, commissioner Zekria Barakzai told reporters.
Barakzai said election officials submitted evidence against these officials to the attorney general and would continue to work to prosecute others.
Associated Press writers Noor Khan in Kandahar and Rahim Faiez, Christopher Bodeen and Heidi Vogt in Kabul contributed to this report.