Addressing reporters after the vote, Foreign Minister Tzipi Livni said the cease-fire deal approved would bring about a "change in the rules of the game" between Israel and Lebanon.
"The decision is good for Israel. I am not naive. I live in the Middle East and I know that not every decision in the Middle East is implemented and yet I still say it's good for Israel. It can lead to the real change in the Middle East that we have all been waiting for."
She noted that "The world now understands that Israel will not accept a terrorist organization on our border firing upon our citizens. We achieved most of our goals. If it's implemented, the change has been dramatic."
Livni also added that "nothing from the UN was forced on us. It was the Foreign Ministry acting for our interest from the first days of the war. When it became clear that the Lebanese government was too weak to enforce its takeover of the south, we asked international forces to come in."
She compared the expected diplomatic situation to the situation before June 12.
Livni urged Lebanese Prime Minister Fuad Saniora and the international community to implement the UN Security Council resolution calling for an end to the fighting and the mobilization of Lebanese troops backed by UN peacekeepers into south Lebanon. She called on the Lebanese army to move into south Lebanon "immediately."
During the press conference, Livni also said Israel would "not neglect" its goal of winning the release of two soldiers whose capture by Hizbullah guerrillas on July 12 precipitated the Mideast crisis.
At the start of the meeting, Prime Minister Ehud Olmert sent his condolences to the families of the fallen and wished for a quick recovery of the wounded. "Our hearts are with all IDF soldiers wherever they are," he said.
Olmert told the ministers that he had met with the families of kidnapped IDF soldiers Ehud Goldwasser and Eldad Regev and that he hoped the captives would now be freed. However, the truce is not linked to the soldiers' release.
The prime minister said he would appoint a senior official to conduct negotiations that would bring about the release of the kidnapped soldiers.
Olmert called the UN Security Council cease-fire resolution a good deal for Israel. According to Olmert, "Hizbullah will no longer exist as a state within a state. Lebanon will be responsible for any problems or violations of the agreement."
Defense Minister Amir Peretz said tough questions would have to be asked after the war. "The war exposed many issues, both regarding the fighting and the home front, that require review and drawing of conclusions," he was quoted as saying.
Peretz told the ministers that the current IDF operation in southern Lebanon would enable the demilitarization of the region and its transfer to the control of the UN and the Lebanese army.
According to Peretz, "The main question is how Hizbullah would react; in any case, we are preparing for all the scenarios."
The defense minister said Israel was holding contacts with UNIFIL in order to establish a mechanism that would coordinate the deployment and IDF withdrawal form southern Lebanon.
UN Secretary General Kofi Annan said in a statement early Sunday that the cease-fire between Hizbullah and Israel would take effect Monday morning, and urged the leaders of Lebanon and Israel to halt fighting immediately.
Annan said in a statement distributed in Lebanon that he had been in touch with Prime Ministers Fuad Saniora and Ehud Olmert to discuss the exact time and date when the cessation of hostilities called for by the 