"It is time for a new Middle East," Secretary Rice told reporters before the start of her talks with Mr Olmert in Jerusalem.
"A durable solution will be one that strengethens the forces of peace and democracy in the region.”
But Israeli Prime Minister Ehud Olmert has said Israel is determined to keep fighting Hezbollah and will take "severe measures" against the group.
Mr Olmert said: "Israel is determined to continue on in the fight against Hezbollah. We will ... stop them.”
”We will not hesitate to take severe measures against those who are aiming thousands of rockets and missiles against innocent civilians for the sole purpose of killing them.”
Israel has demanded that as part of a truce, Hezbollah be dismantled and the Lebanese army be deployed on the Israeli-Lebanese border, but has indicated it would accept an international peacekeeping force in the area.
But the Lebanese government insists there be a truce before a longer-term deal is worked out.
Mr Olmert acknowledged the Israeli offensive had caused humanitarian problems and said he would work with the US to try to
alleviate them.
Some 750,000 Lebanese have been displaced by the fighting, while Secretary Rice said both Israeli and Lebanese civilians were suffering as a result of the fighting.
Secretary Rice, who has called for a ceasefire but not at any price, said "we need to ensure that we will not return to the previous situation."
Peres appeals to Lebanese people
In a speech to Israel's parliament, Israeli Vice Prime Minister Shimon Peres appealed to the Lebanese people to disarm Hezbollah and make peace with Israel.
Mr Peres also said he was certain of victory, saying "in this war, there is no alternative to victory against terrorists. Morally, Hezbollah has already been defeated. It will also be defeated militarily."
In a direct appeal to the Lebanese people, Mr Peres said: "You proved that you could throw the Syrians out of the country, and you can rid your country of the weapons of Hezbollah. This could be your great opportunity.”
"You have at your service an army of 80,000 troops. Where are they?"
He said once Hezbollah was no longer a threat, Israel and Lebanon could make peace.
Ground offensive plans
Meanwhile a senior Israeli army commander has revealed that Israel's ground offensive will not go beyond southern Lebanon.
Outlining the scope of the two-week-old campaign for the first time, the commander, Colonel Hemi Livni, said Israeli forces would focus on trying to destroy outposts and rocket launching sites of Hezbollah guerrillas in southern Lebanon.
"The intention is to deal with the Hezbollah infrastructure that is within reach," Colonel Livni, who commands Israeli troops in the western sector of southern Lebanon, told Israel Army Radio.
"I don't know of any intention to go 70 kilometres into Lebanon," he added.