The abuse described in the report, including details of the deaths of two inmates at an Afghan detention centre, occurred in 2002 and emerged from a nearly 2000-page file of US army investigators, The New York Times reported on Friday.
"It has shocked me thoroughly and we condemn it," Karzai said. "We want the US government to take very, very strong action, to take away people like that."
Karzai, a staunch ally in the US-led war against terrorism, is due to leave on a US trip later on Saturday. He will meet President George Bush for talks next week.
Karzai wants to forge a broad long-term partnership with his most important ally, but said he would reiterate a request for the return of Afghan prisoners and control over US military operations.
The US commands a foreign force in Afghanistan of about 18,300, most of them American, fighting the Taliban and searching for Osama bin Laden.
Many Afghans have criticised US troops for what are seen as heavy-handed tactics, such as breaking into people's homes in the middle of the night.
Growing resentment against US forces was partly behind violent anti-American protests last week, analysts said.
There is growing resentment
against the US in Afghanistan
The protests were sparked by a report that US army interrogators had desecrated the Quran. Sixteen people were killed and many wounded in violence in several Afghan cities.
That report by Newsweek was later retracted, but the International Committee of the Red Cross subsequently said it had told the Pentagon of reports that US personnel had mishandled the Quran in 2002.
Karzai said searches should be carried out in cooperation with Afghan forces.
"No operations inside Afghanistan should take place without the consultation of the Afghan government," he said.
"They should not go to our people's homes any more without the knowledge of the Afghan government ... If they want any person suspected in a house, they should let us know and the Afghan government would arrange that."
Karzai said he would also ask for "the return of prisoners to Afghanistan, all of them".
The US is holding more than 500 prisoners from its war on terrorism at the Guantanamo Bay naval base on Cuba.
Many of them were detained in Afghanistan after US-led troops overthrew the Taliban government in late 2001.
US forces are also believed to be holding several hundred Afghans in Afghanistan.
"They should not go to our people's homes any more without the knowledge of the Afghan government..."
The US army report centres on the death of a 22-year-old taxi driver known only as Dilawar and that of another detainee, Habib Allah, who died at the US base at Bagram, north of Kabul, six days earlier in December 2002.
According to the report, Dilawar was chained by his wrists to the top of his cell for several days before he died and his legs had been pummelled by guards.
Reports of desecration of the
Quran sparked Afghan protests
"The file depicts young, poorly trained soldiers in repeated incidents of abuse. The harsh treatment, which has resulted in criminal charges against seven soldiers, went well beyond the two deaths," The New York Times said.
In sworn statements to army investigators, soldiers described mistreatment ranging from a female interrogator stepping on a detainee's neck and kicking another in the genitals to a shackled prisoner being made to kiss the boots of interrogators, according to the newspaper.
US officials have characterised incidents of prisoner abuse at Bagram in 2002 as isolated problems that were thoroughly investigated, the newspaper said.
Two army interrogators have been reprimanded and seven soldiers have been charged, the newspaper said.