The US secretary of state said she expected the UN Security Council to take up the resolution on Monday or Tuesday, but added: "I want to emphasize it's the first step, not the only step" to halting clashes between Israel and Hezbollah.
"We're trying to deal with a problem that has been festering and brewing in Lebanon now for years and years and years, and so it's not going to be solved by one resolution in the Security Council.
"I would hope that you would see very early on an end to the kind of large-scale violence, large-scale military operations," allowing for the deployment of an international force in southern Lebanon.
"But I can't say that you should rule out that there could be skirmishes of some kind for some time to come."
Rice also sought to ease Lebanese concerns about the resolution after Beirut signalled that the measure must explicitly call for a full Israeli troop pullout from southern Lebanon.
She said: "No one wants to see Israel permanently in Lebanon. Nobody wants to do that. The Israelis don't want it, the Lebanese don't want it, so I think there is a basis here for moving forward.
"I think that the differences here are not very great, obviously Israel would have liked to see other things in this resolution. Lebanon would have liked to have seen other things in this resolution."
Recipe for war
Walid Moallem, the Syrian foreign minister, has said that the US-French ceasefire plan was "a recipe for the continuation of the war."
Moallem was on his first visit to Lebanon since Damascus ended a 29-year military presence in its smaller neighbour last year.
He said an end to fighting required the full withdrawal of Israeli troops before Hezbollah would stop fighting.
The former Syrian envoy to Washington also said his armed forces were under orders to respond immediately if Israel attacked.
After a meeting with Emile Lahoud, the Lebanese president, he said: "If Israel attacks Syria by any means, on the ground, by air, our leadership has ordered the armed forces to reply immediately."