Fogh Rasmussen said the alliance expects a bill of about $4 billion annually to sustain the Afghan fighting forces, which he called a "good deal" since it is cheaper than the cost of war.
But it is not clear that several European governments have the budget or the will to keep paying.
The United States expects to pay much of the cost but U.S. officials say Washington cannot foot the bill alone. Washington wants more nations outside NATO, such as China and Russia, to chip in, arguing that everyone has a stake in ensuring Afghanistan does not slide into chaos.
The United States acknowledges that despite progress the U.S. is not meeting its goal of drawing $1.3 billion annually from other nations for the Afghan armed forces.
U.S. and Afghan officials have already said they expect a shift to an Afghan military lead in combat operations by the middle of 2013, although the U.S. stresses that it will still have a large number of forces in Afghanistan as backup.
Those plans are also expected to be detailed at the Chicago meeting, although without specific details about the pace of the U.S. troop withdrawal.
U.S. military leaders have not submitted final proposals for how to ease nearly 70,000 troops into the back seat next year but are working against a firm deadline to end the current combat mission by 2015.
Afghan Defense Ministry spokesman Gen. Mohammad Zahir Azimi said Wednesday that the Afghans are on track to take the lead in securing the country by the end of 2013. Azimi said the Afghan Army has already reached its target number of 195,000 troops. Including police and other forces, Afghan security forces now number about 330,000.
The combat shift parallels the withdrawal in Iraq, where U.S. forces pulled back from lead roles but remained in harm's way for months before a scheduled end to the war.
Obama also hopes to showcase a long-term security pact with Afghanistan in Chicago. U.S. and Afghan officials said they would like to sign the agreement ahead of the summit, with more specific military agreements to follow.
Karzai raised another condition Tuesday with the request for a written annual commitment. The demand threatens to further delay the key bilateral pact and suggests that Karzai is worried that the U.S. commitment to his country is wavering.