"The Lebanese army, while an absolutely essential part of any solution, is not itself independently capable of dealing with the problem, at least not yet," Snow said.
Snow said the United States was working on another draft resolution, but he would not estimate when a vote might be possible.
"I think at this point it's beyond any of us to come up with a firm prediction about when you get a resolution," he said.
Earlier, French President Jacques Chirac urged the United States to cede quickly to some Arab demands for changes to a UN resolution on ending the Middle East crisis, saying letting the fighting drag on is "immoral."
Caught between US and Arab allies and keen to rescue the diplomatic effort, a Chirac suggested France could even present a new resolution on its own.
Chirac, who interrupted his vacation in southern France to attend an urgent meeting on Lebanon with three Cabinet ministers, appeared frustrated with the US position and keen to placate Lebanon and Arab nations who rejected the original Franco-American draft resolution.
If Paris and Washington do not reach agreement on a new version, he said: "We will have a debate in the Security Council and each will affirm clearly its position, naturally including France, through its own resolution."
The comments at a news conference in Toulon raised the specter of US-French standoffs at the UN Security Council before the Iraq war, though both countries insist they are working for the same goal this time.
"The most immoral of solutions would be to accept the current situation and give up on an immediate cease-fire," Chirac said.
Chirac said an updated version of the draft resolution should take into account Lebanese and Arab demands for changes - but did not specify which ones.
The faltering diplomatic efforts have put Paris in a pinch. France has historic ties to Lebanon and the Arab world, and could lead a proposed multinational peacekeeping force to back up a cease-fire.
A key sticking point is Israeli troops in southern Lebanon. Lebanon wants an immediate pullout, while the United States doesn't want a withdrawal until a new international force is in place, which could take months.
French officials have proposed that before an international force deploys in the Hezbollah strongholds of southern Lebanon, there should be an intermediate step - reinforcing the existing UN peacekeeping mission, UNIFIL, so it could better back up the Lebanese troops.
But the United States has rejected that proposal out of concern that without a new, more robust force in place, a vacuum would be created in Hizbullah territory.
Chirac said the Americans "apparently have reservations" about France's proposed changes to the draft. He also said that French and U.S. officials are in contact daily on how to resolve the conflict.
"That doesn't mean that we agree on everything," he said. "But we are in permanent contact."
The French president provided no details of his talks Wednesday with Prime Minister Dominique de Villepin, Defense Minister Michele Alliot-Marie and Foreign Minister Philippe Douste-Blazy.
