Olmert acknowledged "humanitarian difficulties" caused by Israel's two-week military campaign in Lebanon, and said Israel would work with the US to try to solve some of those problems.
"We are aware of the state of humanitarian affairs of the population of Lebanon as a result of the brutality of Hizbullah," the prime minister added. "I think I can say in complete sincerity that Lebanon and Israel are both victims of this brutal terrorist, murderous organization."
Rice was scheduled to meet on Tuesday afternoon with Defense Minister Amir Peretz, before going to Ramallah for a meeting with Palestinian Authority Chairman Mahmoud Abbas.
She is scheduled to leave Israel Tuesday evening for an international conference in Rome that will deal with the Lebanese situation.
Rice held a late night meeting with Foreign Minister Tzipi Livni in Jerusalem on Monday aimed at creating conditions for a sustainable cease-fire.
Rice's visit, and her meeting with Livni, were delayed some two hours because of a five-hour surprise visit to Lebanon.
Before entering the meeting with Livni, Rice said, "Every peace has to be based on enduring principles" and that "ultimately, a Middle East that is peaceful and democratic will be a place where peace is sustainable."
Senior officials in Livni's office said the talks would center on coming up with a formula for the intervention of the international community that would ensure the release of the captured IDF soldiers, the implementation of UN Security Council Resolution 1559 and the principles laid down recently by the G-8.
Israeli diplomatic officials said the discussions in Jerusalem would also address Iran's involvement in the current crisis, the situation in Gaza and the humanitarian crises there and in Lebanon.
One focus will be the idea of dispatching an international force to help the Lebanese army assert control over south Lebanon and the border with Syria. Both the composition and mandate of this force need to be worked out.
Before coming to Jerusalem, Rice praised Lebanese Prime Minister Fuad Saniora in Beirut for his "courage and steadfastness." Nevertheless, there were signs that her trip there disappointed Lebanese leaders.
Saniora told Rice that Israel's offensive was taking his country "backwards 50 years" and called for a "swift cease-fire," his office said.
Rice also met with Lebanese Parliament Speaker Nabih Berri, who is close to Hizbullah and considered friendly to Syria. An official close to Berri said he did not reach agreement with Rice because she wanted a comprehensive package to halt the fighting and diminish Hizbullah's strength, rather than an immediate cease-fire.
Reuters quoted a Lebanese political source as saying that Rice told Berri, "The situation on the border cannot return to what it was before July 12."
Bush administration officials have said a cease-fire would be premature unless it addressed the threat Hizbullah posed to Israel and the Islamist organization's domination of south Lebanon.
Going into the session at Berri's lavish office and residence, Rice said, "I am deeply concerned about the Lebanese people and what they are enduring. I am obviously concerned about the humanitarian situation."