"Any peace is going to have to be based on enduring principles and not on temporary solutions," said Rice just before holding a meeting with Livni in Jerusalem.

The top U.S. diplomat also lent sympathy to the Israeli, Lebanese and Palestinian people.

"This is a difficult time for the Israeli people, it is a difficult time for the Lebanese people, it is a difficult time for the Palestinian people," she said.

"Ultimately, a Middle East that is peaceful and democratic will be a place where peace is sustainable," she added.

Describing Rice's visit as "very important", Livni reiterated that Israel had the right to protect its citizens.

In the wake of an unannounced brief visit to Lebanon, Rice arrived in Tel Aviv and reached Jerusalem on Monday night.

The senior U.S. official, on her first Mideast tour since violence between Israel and Hezbollah erupted on July 12, is also planned to meet Israeli Prime Minister Ehud Olmert at 9:00 a.m. (0600 GMT) in Jerusalem on Tuesday.

She is also expected to hold talks with Palestinian President Mahmoud Abbas.

During her Beirut visit, Rice met with Lebanese Prime Minister Fouad Siniora and Parliament Speaker Nabih Berri, insisting on Hezbollah's release of the two Israeli soldiers and withdrawal from the border with Israel before any ceasefire.

The United States has justified Israel's massive assault in Lebanon, refusing to back an immediate ceasefire which it said would only lead back to the status quo.

The massive Israeli assault in Lebanon, launched following the capture of two Israeli soldiers by Hezbollah in cross-border attacks on July 12, entered the 13th day on Monday.

On another front, the Israeli army continued an almost one-month-old air and ground operation in Gaza to free another Israeli soldier abducted by Palestinian militants and halt Palestinian rocket attacks.