In a statement issued by his office, Karzai expressed "concern at the coalition forces' decision to bomb civilian areas" at Azizi village in Kandahar but also strongly condemned the "terrorists' act of cowardice" in using civilians as human shields.
Karzai is on an official visit of the United Arab Emirates. The statement said that on his return to Kabul, he would summon the commander of U.S.-led coalition forces in Afghanistan for a "full explanation."
The coalition said 20 Taliban were confirmed killed in the air strike on Azizi late Sunday or early Monday, while up to 60 more militants may have died. It said it was looking into reports of civilian casualties. Karzai's statement said 16 civilians were killed.
In new fighting, Taliban militants on Monday ambushed a police patrol in southern Afghanistan, killing three police but leaving 12 militants dead, officials said. Also three health workers and their driver were killed by a land mine near the capital.
According to Afghan and coalition figures, the deaths brought the number of people reported killed in fighting during the last week to 305. Most of the dead were militants. It's the deadliest spate of fighting in four years and comes ahead of preparations for the U.S.-led coalition to hand over security operations in southern Afghanistan to NATO by July.
At Azizi, where religious schools and mud-brick homes were hit by the air strike, angry villagers buried their dead. One villager, Haji Ikhlaf, told The Associated Press that 26 civilians had been buried by early Tuesday — higher than the toll given by officials.
"We've buried women. We've buried children," Ikhlaf, 40, said by cell phone from the area, which has been closed off to reporters by local security forces. "They are killing us. We are so angry."
Villagers also dug graves of slain Taliban rebels, he said.
U.S. commander Lt. Gen. Karl W. Eikenberry told the AP on Monday that the military was "looking into" reports of civilian deaths. Other coalition officials said they were confident they had hit a Taliban compound.
Monday's ambush against police occurred in Helmand, a province neighboring Kandahar and heartland of the country's multibillion dollar heroin trade.
Ghulam Muhiddin, the provincial administrator, said dozens of Taliban fled after the attack, leaving the bodies of 12 fighters behind. Police reinforcements were rushed to the area and also found several assault rifles, machine guns and rocket launchers.
The medical workers were killed Monday about 40 kilometers (25 miles) west of Kabul on a busy road often frequented by foreigners, said Bashar Gul, a local deputy police chief.
The blast killed a doctor, two nurses and their driver, he said. The four worked for the local Afghan Health Development Services.
Militants have repeatedly targeted aid workers, including doctors and teachers. Last month, gunmen stormed a medical clinic in a northwestern province and killed five doctors and nurses.
The Taliban opposes the presence of the development workers because they believe they bolster Karzai's U.S.-backed government.
Militant supporters of the former regime have stepped up attacks this year, drawing a tough response from coalition and Afghan government forces.
The coalition air strike on Azizi was the third clash there in a week. U.S. Air Force A-10 Warthog warplanes bombed an Islamic school, or madrassa, where the militants were suspected of hiding, before hitting surrounding homes as the insurgents took shelter.
Up to 27 militants were killed in a ground battle and air strike in the same area Thursday.