A row between the US and Pakistan over supply routes to Afghanistan is threatening to overshadow the summit of Nato leaders in Chicago.
The two sides have been unable to reach agreement on Pakistan's conditions for reopening the routes, closed after a US air strike killed many troops.
Leaders from more than 50 nations have held a key meeting to discuss the future strategy for Afghanistan.
US President Obama said: "As Afghans stand up, they will not stand alone."
Nato Secretary General Anders Fogh Rasmussen, opening Monday's meeting, confirmed plans to hand over full combat command to Afghan forces by mid-2013.
He also confirmed that Nato-led forces would complete their combat role by the end of 2014.
The nations represented at the summit include heads of state and government from the 28 Nato countries, along with Afghan President Hamid Karzai and Pakistani President Asif Ali Zardari.
But as the heads hammered out a strategy for Nato's future involvement, the problem of supply routes from Pakistan remained unresolved, despite a meeting between Mr Zardari and US Secretary of State Hillary Clinton on Sunday evening.
The supply route was closed in November after a US drone attack killed many Pakistani troops.
But in return for reopening the routes, Pakistan has called for:
A public apology for the killings
A review of US policy on drone attacks inside Pakistan
A large increase of the current transit charge of $250 (£158) per vehicle.
US Defence Secretary Leon Panetta said before the summit that it was "not likely" that the US would be prepared to pay the higher amount demanded by Pakistan.
Correspondents say Mr Obama is unhappy about the fee, given that US is already giving Pakistan large amounts of aid.
US officials say no bilateral meeting is being planned between Mr Zardari and Mr Obama.
After Monday's meeting, UK Prime Minister David Cameron said the situation was "frustrating" and that although he was confident the supply routes would be reopened, it was "not going to happen today".
In its summit declaration, Nato simply says it "continues to work with Pakistan to reopen the ground lines of communication as soon as possible".
It adds: "The countries in the region, particularly Pakistan, have important roles in ensuring enduring peace, stability and security in Afghanistan and in facilitating the completion of the transition process.
"We stand ready to continue dialogue and practical cooperation with relevant regional actors in this regard."
In his remarks ahead of the Afghan meeting, Mr Obama said the Nato mission was "truly international".
He said: "The region and the world have a profound interest in an Afghanistan that is stable, secure and not a source of attacks on other nations."
Mr Obama said important progress had been made.
He said: "We have broken the Taliban's momentum. Afghans have grown stronger and the transition is well under way."
One key issue for discussion has been the funding of the transition.
Washington is expected to pay half of an estimated $4bn (£2.5bn) needed every year.
Nations at the summit have pledged another $1bn towards the costs, although Mr Cameron said more countries should step up and contribute.
Differences on troop withdrawals still have to be hammered out.
France says that its troops will return by the end of 2012.
President Francois Hollande said the issue was "non-negotiable because it was a question of French sovereignty".
More than 10 years after the US toppled the Taliban regime, violence is continuing unabated in Afghanistan. According to UN figures, the number of deaths reached a record 3,031 in 2011 - the great majority caused by militants.