6 March 2011 Last updated at 10:47 ET
President Hamid Karzai has told the US commander of foreign troops in Afghanistan that his apology for the deaths of nine children in an air strike is "not enough".
"On behalf of the people of Afghanistan I want you to stop the killings of civilians," Mr Karzai said at a cabinet meeting attended by Gen David Petraeus.
The children were killed in a Nato strike on Tuesday.
Hundreds of people rallied on Sunday to denounce the killing of civilians.
The issue of civilian casualties is a source of widespread public anger and of tension between the Afghan government and the US, the BBC's Jill McGivering reports.
Washington is well aware of the strength of feeling and has worked hard to reduce casualties, she adds, though Nato says most civilian casualties last year were caused by Taliban insurgents, not the security forces.
On Sunday, at least 12 civilians, including five children, were killed by a roadside bomb in eastern Afghanistan.
'Stop the killings'
"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 relationships between Afghanistan and the US," President Karzai was quoted as saying.
"The people are tired of these things and apologies and condemnations are not healing any pain."
On Wednesday, Gen David Petraeus said he was "deeply sorry" for the air strike in which the boys, aged 12 and under, were mistaken for insurgents by Nato helicopters as they gathered firewood.
Sunday's rally in Kabul condemned both Nato and the Taliban for killing civilians.
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