US Secretary of State Condoleezza Rice is to meet Israeli and Lebanese leaders after returning to the region for the second time in a week.
The UN is set to discuss deploying a new force in Lebanon
She says "there will have to be give and take" as both sides will be forced to make "hard and emotional decisions".
The Hezbollah militia has dismissed Ms Rice's visit and warned of more missile attacks reaching deeper inside Israel.
At least 20 casualties are reported in an Israeli air strike on a building in the southern Lebanese town of Qana.
The Lebanese Shia militia's leader, Hassan Nasrallah, said Ms Rice had returned to serve the interests of the US and Israel.
"There are many cities in central Israel which will come into target range... if the barbaric aggression on our country and people continues," Mr Nasrallah said in a televised address.
The UN says some 600 people - about a third of them children - have been killed by Israeli action in Lebanon.
Hezbollah has continued firing hundreds of rockets into Israel - several hit the northern Israeli town of Safed on Saturday.
A total of 51 Israelis, including at least 18 civilians, have been killed in the conflict, sparked by Hezbollah's capture of two Israeli soldiers in a cross-border raid earlier in July.
On Saturday night, Ms Rice held a private dinner meeting with Israeli Prime Minister Ehud Olmert.
The UN says 600 Lebanese people have died
She is expected to meet Israeli defence and foreign ministers on Sunday, before travelling to Beirut to meet the Lebanese government.
Talks will raise a possible new UN Security Council resolution that would enable the deployment of peacekeepers.
"I expect the discussions to be difficult, but there will have to be give and take," Ms Rice said on Saturday.
"I assume and have every reason to believe that leadership on both sides of this crisis would like to see it end," she said.
According to BBC correspondent Jonathan Beale, Ms Rice has revealed little of her proposals to end the violence.
He says her meetings will seek to accumulate support for a new UN Security Council resolution.
Deployment of a large international force is expected to be discussed by world leaders at a meeting at the UN headquarters in New York on Monday.
The US has already stated that it expects Lebanon's government to take steps to rein in Hezbollah.
Israel has been battling Hezbollah fighters in southern Lebanon
Less clear, though, is how Israel will fulfil its side of the bargain, our correspondent says.
Israeli officials have indicated to the BBC that Israel may be willing to stop fighting as soon as a UN resolution is passed next week - before the arrival of any new peace force - and that they will not insist on Hezbollah disarming first.
They insist, however, that such a force must have the authority to disarm Hezbollah and cut off its weapons supplies.
An Israeli air strike on Saturday closed the main border crossing from Lebanon into Syria, witnesses and officials say.
Missiles hit the road between the two states' immigration posts, but on the Lebanese side, the reports said.
A separate strike wounded two UN monitors in their observation post, the UN said, days after four were killed.
Even before the latest UN casualties, the UN had warned that the deaths of the four monitors could deter countries from contributing to the proposed peacekeeping force.
Lebanon's latest dead include a mother and her five children killed in a wave of Israeli air raids in the south of the country, doctors said. Israel said it was investigating the report.
On Saturday Israeli forces withdrew from the southern Lebanese village of Bint Jbeil - a Hezbollah stronghold - which they had been trying to take for some days and where they sustained their heaviest one-day losses since the campaign began.
Earlier, Israel rejected a UN call for a three-day truce in southern Lebanon.
The UN said children, the elderly and disabled people were trapped and supplies were short, but Israel said there was no need for a truce as a humanitarian corridor to the area had been opened.