Asked what such a partnership would entail, he replied: "Economic assistance, technical assistance, military partnership including - and this is a personal view - joint military permanent bases and also cultural exchanges."
He said the arrangement would be "not only for the good of the Afghan people, but also for the good of the American people because of the long-term security interests that we have in the region."
McCain was leading a five-member delegation also including former first lady Senator Hillary Clinton, as well as senators Russell Feingold, Susan Collins and Lindsey Graham.
McCain did not elaborate about what form permanent bases might take and Karzai gave no further details after the meeting.