President Karzai says he’ll ask President Bush for more say over military operations in his country, including an end to raids on the homes of Afghans unless his government was notified beforehand.
Mr Karzi also plans to ask for greater assistance in the fight against drug cultivation.
The abuse by US troops centres around the US-run military prison of Bagram, north of Kabul. It has been reported that two Afghan prisoners died at the centre from apparent beatings in 2002.
Anti-US riots broke out across the country earlier this month, leaving at least 15 people dead.
“I am here to ask President Bush for a longer-term relationship with Afghanistan, for a strategic partnership with Afghanistan, that will involve economic support, military support and security assistance,” President Karzai said on Sunday.
“What I asked for was that the prisoners of Afghanistan to come back to Afghan prisons from US detention and moving towards a better future.
“The nation of (Afghanistan) has changed since there is a stronger ownership of the Afghan government and the Afghan people now,” he said.
Eight Afghan prisoners have so far died in US custody in Afghanistan, although no US personnel have yet been charged.
President Karzai also said his government was actively seeking Al-Qaeda leader Osama bin Laden who is still on the loose.
Since helping to bring down the Taliban in 2001, Washington has remained President Karzai’s biggest supporter, both in terms of reconstruction aid and military security, with 18,000 troops on the ground fighting an increasingly deadly insurgency.
The issue of drug production in Afghanistan is also on the agenda.
Citing a secret report, the New York Times reports the US State Department has blamed the Afghan leader of not having done enough to battle increased opium cultivation.
“Although President Karzai has been well aware of the difficulty in trying to implement an effective ground eradication program, he has been unwilling to assert strong leadership, even in his own province of Kandahar,” the newspaper quoted the document as saying.
However, President Karzai said areas under Afghan government control had reduced opium poppy growth, while areas where production had risen were under the control of foreign countries, especially Britain.
“The failure is theirs not ours,” he told CNN.
During his four-day visit to the United States, Mr Karzai will also meet US Vice President Dick Cheney, Secretary of State Condoleezza Rice and the new head of the World Bank, Paul Wolfowitz.
He will also meet members of Congress, whose job is to approve the multi-billion dollar packages of military and economic aid that are stopping Afghanistan from becoming a failed state.
The US is contributing $US15b (A$20b) a year to Afghanistan, 80 per cent of the total going towards military expenses.