But in a joint news conference in Kabul on Wednesday, both he and visiting US Defence Secretary Donald Rumsfeld sidestepped questions as to whether this would involve permanent US bases.
Asked if permanent US bases were planned, Karzai said the Afghan people wanted "a longer-term relationship with the United States" after 30 years of war and upheaval.
"They want this relationship to be a wholesome one, including a sustained economic relationship, a political relationship and, most important of all, a strategic security relationship that would enable Afghanistan to defend itself."
Stronger military ties
Karzai said: "I have already raised it with President Bush in Washington on my previous trips. And Afghanistan is requesting, seeking, such a partnership, yes.
"A request in this regard will be sent to President Bush."
Washington has been seeking stronger military ties with other countries in Central Asia that would include transit rights and the right to stockpile weapons.
"That is not a matter
for the Department
of Defence; that is a matter for the resident
of the United States
and the president of Afghanistan to discuss
in an orderly way"
US Defence Secretary
Rumsfeld said military relations between the US and Afghanistan were strengthening and Washington was thinking more about the type of help it could offer, rather than bases.
"It may be training, it may be equipping, it may be various other types of assistance," he said. "But we think more in terms of what we're doing, rather than the question of military bases."
Pressed on what an agreement with Afghanistan might entail and whether it could include permanent bases, Rumsfeld said: "That is not a matter for the Department of Defence; that is a matter for the president of the United States and the president of Afghanistan to discuss in an orderly way."