Afghan President Hamid Karzai on Sunday told US General David Petraeus, the commander of international troops, that his apology after nine children died in a NATO air strike was "not enough".
Hundreds of angry demonstrators also rallied in central Kabul over the deaths in an air raid by coalition helicopters in the eastern province of Kunar on Tuesday.
NATO's International Security Assistance Force (ISAF) said the children -- who were collecting firewood in the province's Dar-e-Pech district when they were killed -- were mistaken for rebels.
Petraeus and US President Barack Obama both apologised.
The Western-backed Karzai, who has shaky relations with Washington, had already condemned the deaths, but on Sunday addressed Petraeus directly at a cabinet meeting at which the US general was present.
"President Karzai said that David Petraeus's apology is not enough," a statement from the Afghan presidency said.
"The civilian casualties are a main cause of worsening the relationship between Afghanistan and the US," the statement quoted Karzai as saying.
"The people are tired of these things and apologies and condemnations are not healing any pain.
"On behalf of the people of Afghanistan I want you to stop the killings of civilians."
The air strike that killed the children was against insurgents who had attacked a military post, but it hit the young victims by mistake, according to military officials.
Civilian casualties -- especially involving children -- are a highly sensitive issue in war-torn Afghanistan, where a Taliban-led insurgency has raged since the Islamists were ousted from power by a US-led 2001 invasion.
Karzai says deaths of civilians in military operations turn people against his delicate pro-US administration. Civilian casualties have also been a key source of tension between Kabul and its Western backers, the US and NATO.
A week before the children were killed, Karzai said troops had killed 65 non-combatants during operations in Kunar province's Ghaziabad district.
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That was followed by another incident in which Afghan authorities said troops killed six civilians in neighbouring Nangarhar province, also in an air raid.
About 500 people poured onto the streets of Kabul earlier on Sunday and chanted anti-American slogans over the deaths of the children.
Marching through central Kabul they shouted "Death to America -- Death to the invaders." A placard carried by a veiled woman read: "Occupation = killing + destruction."
"We don't want the invading forces," chanted one demonstrator carrying posters of the dead children. Another shouted: "Death to the government of President Hamid Karzai!"
"When I saw the demonstration and realised it is against the Americans I joined," Azizullah, one of the protesters, who uses one name, told AFP.
Also Sunday, a roadside bomb ripped through a car in eastern Afghanistan, killing 12 civilians.
The Taliban-style home-made device struck the car in the province of Paktika, killing five children, two women and five men, the provincial administration said in a statement.
The victims were on their way from neighbouring Pakistan, it said, without giving further details.
Mohibullah Samim, the provincial governor, blamed the bombing on "enemies of peace who once again revealed their tyrant face to the public," the statement added.
Rebels loyal to the Taliban and other militant groups often use improvised -- or home-made -- bombs in attacks against Afghan security forces and their Western military backers.
There are about 140,000 foreign military forces operating in Afghanistan under the command of Petraeus.
Bombs are usually planted on public roads and often kill civilians instead of their military targets. A similar device on February 26 killed nine civilians in Khost province, which borders Paktika.