The delay until next week apparently would give the French time to negotiate privately with the United States, the most vocal opponent of the international tribunal, and avoid a potentially embarrassing veto.
Axel Cruau, spokesman for the French mission at the United Nations, said there was still room to negotiate with Washington.
"I can't say who said it and at which level, but we had some information that with forward talks and the prospect of more time, the chances to avoid the veto and for a resolution would be greater," Cruau said.
In Washington, Adam Kreli, a State Department spokesman, said there were still a number of ideas, including the French one, that "merit discussion."
Secretary of State Condoleezza Rice spoke to her French counterpart, Michel Barnier, over the issue, he said. He added the United States will work with France toward a "positive outcome."
2014: The Year in Music [PHOTOS]