Rice, who has just ended a diplomatic mission to the region, said she was returning to Washington with "an emerging consensus on what is necessary for both an urgent ceasefire and a lasting settlement".
She said, "I am convinced we can achieve both this week and I am convinced that only by achieving both will the Lebanese people finally be able to control their country and their future and the people of Israel will finally be able to live free from the threat of attack from terrorist groups in Lebanon."
The US secretary of state did not provide details on what both sides may have agreed, although a meeting of potential troop contributors to an international force is to be held on Monday at the UN.
Rice has said the force should be deployed as soon as possible after any UN resolution is passed.
Her comments come a day after Israel provoked international outrage following the bombing of a building in the village of Qana in southern Lebanon which killed at least 50 civilians, most of them children.
After the bombing Fouad Siniora, the Lebanese prime minister, cancelled talks with Rice in Beirut, saying he could not hold diplomatic talks until an "immediate and unconditional cease-fire" was announced.
Emile Lahoud, the Lebanese president, told Aljazeera that the current offensive was a "pre-organised US plan, implemented by Israel" and revenge for Israel's withdrawal from Lebanon in 2000 after 18 years of occupation.
He also rejected the deployment of a multi-national peacekeeping force, calling instead for a cease-fire and the reinforcement of existing international troops.
The United Nations Security Council said in a statement that it "strongly deplores" the attack on Qana, but stopped short of calling for an immediate end to the fighting after Washington forced the Council to water down its language.
"The Security Council expresses its concern at the threat of escalation of violence with further grave consequences for the humanitarian situation," said the statement issued on Sunday.
"The Security Council expresses its concern at the threat of escalation of violence with further grave consequences for the humanitarian situation"
UN statement on Qana bombing
Kofi Annan, the UN secretary general, had urged the Council to call for an immediate ceasefire and warned Israel and Hezbollah they were both likely guilty of "grave breaches of international humanitarian law".
"I'm deeply dismayed that my earlier calls for immediate cessation of hostilities were not heard, with the result that innocent lives continue to be taken," he said on Sunday.
Dan Gillerman, Israel's ambassador to the UN, told the Security Council that Qana was "a hub for Hezbollah" and said Israel had urged villagers to leave.
However, Lebanon said Israeli air strikes on roads and vehicles had rendered escape impossible for people in the south.
Israel on Monday halted its airstrikes for 48 hours pending an investigation into the bombing, although Haim Ramon, the Israeli justice minister, told army radio it that the stoppage "does not signify in any way the end to the war".
Israel is also to co-ordinate with the UN to allow a 24-hour window for residents of southern Lebanon to leave the area and allow much-needed humanitarian aid to enter.
Lebanon's health minister said up to 750 people, most of them civilians, have been killed by Israeli military action since the conflict began.
A total of 51 Israelis, including at least 18 civilians, have been killed by rockets fired into Israel by Hezbollah fighters.
The conflict began on July 12 when Hezbollah fighters began firing rockets into northern Israel and captured two Israeli soldiers in a cross-border attack.