The two sides have been unable to reach agreement on Pakistan's conditions for reopening the routes, closed after a US air strike killed several troops.

The summit goes into a second day with troop withdrawals from Afghanistan dominating the agenda.

France insists 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".

The handover is expected to be completed by 2014, but several other Nato leaders are under domestic political pressure to bring troops home earlier.

More than 50 leaders are attending the summit, including heads of state and government from the 28 Nato countries, along with Afghan President Hamid Karzai and Pakistani President Asif Ali Zardari.

The summit is expected to endorse plans to hand over combat command to Afghan forces by mid-2013 and seek progress in opening routes for troop withdrawals.

They also hope to reach a commitment on who pays how much towards funding Afghan forces after 2014.

Some nations - including the US, Australia, Britain, and Germany - have pledged to contribute to an international fund to help Afghan forces after the Nato pullout.

Washington is expected to pay half of an estimated $4bn (£2.5bn) needed every year.

The US invited Mr Zardari to the summit, in the hope of signing a deal to reopen the Pakistan-Afghanistan border to US transport.

The route was closed in November after a US drone attack killed several Pakistani troops.

But in return for reopening the routes, Pakistan has called for:

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 US President Barack 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, although the Pakistani leader met Secretary of State Hillary Clinton on Sunday evening.

Chicago is braced for more protests for the second day of the summit, with more than 20 underground stations closed and buses re-routed.

The Occupy Chicago movement is planning a rally outside the building that houses the offices of Boeing, which it accuses of avoiding tax payments because of its work for the military.

On Sunday, dozens of protesters were arrested after being kept from the summit's convention centre.

As talks began on Sunday, President Obama spoke of a "transformational decade" in Afghanistan and the enormous sacrifices of the American people on the road to peace, stability and development.

He warned there were still "great challenges ahead", urging leaders to "pool resources".

Nato Secretary General Anders Fogh Rasmussen said there would be "no rush for the exits" and the mission would shift from combat to support.

The BBC's defence correspondent Caroline Wyatt says the summit is seeking to reconcile two different messages.

It is telling the public in Nato countries that the fighting in Afghanistan is coming to an end for their troops, while reassuring the Afghans that the alliance will not abandon them after 2014, our correspondent says.

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.