At an Oval Office meeting, Obama and Rasmussem agreed the summit would be a time "reaffirm allied commitment to the transition framework" and a move from a combat role to support for "sufficient and sustainable Afghan forces."
At the summit, Nato will be faced with the thorny issue posed by French president-elect Francois Hollande pledge to speed up his country's pullout from Afghanistan.
The French Socialist leader campaigned on a promise to start bringing 3,300 French soldiers home this year, ending his country's combat role two years earlier than Nato's carefully crafted plan to fully hand security control to Afghans by 2014.
The White House has said the United States will push to modernize the North Atlantic Treaty Organization, deepen partnerships and hammer out details of the Afghanistan withdrawal at an summit.
Some 130,000 foreign troops, most from Nato nations, are fighting alongside 350,000 Afghan security personnel to help Afghan President Hamid Karzai's government reverse the Taliban-led insurgency.
Obama and the Nato chief also discussed the importance of Nato's partnerships with non-Nato countries, and agreed the summit should be a venue to highlight the need for allies to field Nato's defense capabilities in the future.
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Is Pakistan taking part in NATO summit in Chicago? It would spoil the Afghan end-game if it stays away from this meeting!