US Secretary of State Condoleezza Rice has expressed concern for the suffering of "innocent people" in the current fighting in the Middle East.
Israel has continued to bombard southern Lebanon
She was speaking after talks with Palestinian President Mahmoud Abbas and following an earlier meeting with Israeli PM Ehud Olmert.
Mr Abbas called for an immediate truce but Mr Olmert told her there would be no let-up in army operations.
Ms Rice did not back Mr Abbas' call - but urged peace across the region.
Ms Rice's diplomatic tour comes as Israeli forces continue operations in Lebanon and the Gaza Strip.
They have resumed bombing targets in Beirut - after a lull during Ms Rice's visit on Tuesday.
Some 380 Lebanese and up to 40 Israelis have died in nearly two weeks of conflict in Lebanon, which began after Hezbollah captured two Israeli soldiers in a cross-border raid on 12 July.
Another soldier was seized by Palestinian militants earlier.
After meeting Mr Abbas in Ramallah on the West Bank, Ms Rice said: "I assured the president that we have great concerns about the suffering of innocent peoples throughout the region."
Mr Abbas called for an immediate end to "aggression against the Gaza Strip and the West Bank" and for an "immediate ceasefire" in Lebanon.
Ms Rice said the only solution was a sustainable peace - "one that can deal with the causes of extremism and lead to the establishment of sovereignty for the Lebanese government throughout its territory".
As Ms Rice continued her diplomatic shuffle, Israel maintained its operations in Lebanon, sealing off Bint Jbeil, a Hezbollah stronghold which has been the scene of a fierce battle since the Israelis took the nearby village of Maroun al-Ras on Saturday.
A number of Hezbollah militants are believed to be holding out in the town.
Israel has been carrying out heavy shelling, but Hezbollah guerrillas are still managing to fire their Katyusha rockets.
A 15-year-old Arab-Israeli girl was killed when a rocket hit her house in the northern Israeli village of Maghar.
Ms Rice had not been expected to openly criticise Israel
Haifa, Israel's third largest city, has been hit by at least a dozen rockets fired from inside Lebanon. An elderly man died of a heart attack as he tried to take shelter.
The Lebanese coastal city of Tyre is seeing heavy Israeli bombardment of the hills south of the city both from Israel and from the sea.
Further north, seven members of one family, including two children, were killed in an overnight air strike in the town of Nabatiyeh.
Saudi Arabia's King Abdullah has appealed to the world to stop the Israeli offensive saying that if not it could engulf the entire Middle East in war.
'New' Middle East
In his meeting with Ms Rice, Mr Olmert said he was "very conscious" of the humanitarian needs of Lebanon's civilians, but insisted Israel was defending itself against terrorism.
He said Israel was not at war with the Lebanese people, but with Hezbollah, which he described as a terrorist organisation, insisting that Israel would take the "most severe measures" against it.
Correspondents say that Ms Rice was unlikely to have called for an end to Israel's military offensive during her talks with the Israeli leader.
The BBC's World Affairs Editor John Simpson, in Jerusalem, says it was understood that Ms Rice would tell Israel that the US will allow it more time to continue its military operations.
Ms Rice has, however, also been highlighting the need for Israel to consider the humanitarian needs of both Lebanon and the Palestinian people and the need for a durable peace.
She said: "It is time for a new Middle East, it is time to say to those who do not want a different kind of Middle East that we will prevail; they will not."
Ms Rice arrived in Israel from Beirut, where she met Lebanon's Prime Minister Fouad Siniora.
Correspondents say there is disappointment in Lebanon that the talks did not result in more concrete action and calls for an immediate ceasefire.