Obama and the 27 other NATO leaders Friday in their first get-together were to adopt a new strategic concept, the alliance's first in more than a decade. It won't renege on the nuclear deterrent but could include a pledge, lobbied for by several European governments, to reduce and eventually eliminate nuclear weapons.
In talks Saturday, the United States and its allies are also expected to coordinate the strategy for Afghanistan, where NATO has some 150,000 troops, about two-thirds of them from the United States.
The alliance aims to hand over full security responsibility to Afghan authorities by the end of 2014. Obama, who is to meet Afghan President Hamid Karzai Saturday, has said U.S. troops will begin withdrawing next July.
U.S.-Afghan relations have taken a hit over an increase in U.S.-led night raids that American military officials say play a key role in driving back the Taliban. Karzai, however, wants the raids to stop because they claim civilian casualties.
The alliance's restart of relations with Russia should feature high on the agenda of the Lisbon summit, which is the first involving Russia since its 2008 war with Georgia, a former Soviet republic.
NATO-Russia relations are closely linked to another key element of the new concept, a missile defense system based in Europe, possibly Romania or Turkey, to defend against a possible attack from Iran. Moscow had in the past labeled the system a threat to its security but has since been appeased by U.S. offers to include Russia in the planning.
NATO Secretary-General Anders Fogh Rasmussen said he hoped to win Russia's approval for more cooperation also in Afghanistan.
NATO wants Russia to "broaden the existing agreement on transit," to allow land movement to and from Afghanistan, Rasmussen told Russian news agency RIA Novosti.
He added NATO would like Russia to help the Afghan armed forces operate their Russian-built helicopter fleet more efficiently, by offering training and spare parts.
Finally, "we will most certainly increase the scope of our joint training for counter-narcotics experts from Afghanistan and neighboring countries," Rasmussen said.
After the summit's final declaration Saturday, Obama is to meet with European Union leaders as the 27-member body is dealing with debt crisis plaguing eurozone members Ireland, Greece and summit host Portugal.