"From the statements made by US officials, US senators to the media and from what they have told us, yes, they have this desire," Karzai said.
However, Karzai has insisted that Afghanistan would have the final say on whether such bases would be allowed or not.
In January, influential US senator Lindsey Graham had reportedly suggested permanent US bases in Afghanistan. At that time, Karzai's spokesman Waheed Omer said the issue had not been discussed with the United States.
The US embassy in Kabul referred media queries on the issue to the US-led NATO military in Afghanistan, the International Security Assistance Force (ISAF), was not immediately available for comment.
There are around 140,000 international troops and two-thirds of them from the United States which are fighting Taliban insurgents in Afghanistan.
Afghan forces are due to take responsibility for security from 2014, allowing international troops to pull back.
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