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.
AFP news agency quoted new President Francois Hollande as saying 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 President Karzai and 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.
Pakistan’s ruling PPP party appears to be in a difficult spot over the issue of the reopening of the overland Nato supply routes into Afghanistan. There are many internal pressures.
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.