A NATO air strike killed a family of eight, including six children, when it ploughed into their home in Paktia, local officials said on Sunday.
"Eight people, a man, his wife and six of their children, are dead," local government spokesman Rohullah Samoon told AFP.
"It was an air strike conducted by NATO. This man had no connection to the Taliban or any other terrorist group."
A senior security official in Kabul confirmed the strike and deaths.
"It's true. A house was bombed by NATO. A man named Mohammad Sahfee, his wife and six of their innocent children were brutally killed," the official said.
A spokesman for NATO's International Security Assistance Force (ISAF), Lt-Col Jimmie Cummings, said it was investigating the claim.
Karzai, who signed a long-term strategic pact with President Barack Obama this month, argues that civilian deaths caused by allied troops turn common Afghans against his Western-backed government.
Karzai summoned ISAF commander General John Allen and US ambassador Ryan Crocker to the presidential palace just over two weeks ago after a number of civilians were killed in NATO airstrikes.
NATO and US forces in Afghanistan admitted in a joint statement after the meeting that civilians had died in two separate hits.
The statement gave no details of how many civilians died in each of those incidents but local officials put the total at more than 20, including women and children.
"The president will be assured of our commitment to take any and all appropriate actions to minimise the likelihood of similar occurrences in the future," the statement said.
The number of civilians killed in Afghanistan's war has risen steadily each year for the past five years, reaching a record of 3,021 in 2011, the great majority caused by militants, according to UN statistics.
NATO has some 130,000 troops in Afghanistan, mostly from the United States, but they will withdraw by the end of 2014.