US Secretary of State Condoleezza Rice has held talks with Lebanon's PM in Beirut at the start of a Middle East tour to discuss the regional crisis.
She met Fouad Siniora on an unannounced visit that her officials said was to show support for Lebanon's people.
Ms Rice praised Mr Siniora's "courage" but has also said there is no place for "terrorist groups" like Hezbollah to attack from Lebanese territory.
She has now arrived in Israel for talks with Prime Minister Ehud Olmert.
In the latest developments:
- Israeli forces pushed north from the captured village of Maroun al-Ras in south Lebanon and fierce clashes were reported around Bint Jbeil. Ten Israeli soldiers were hurt in the border fighting and two Hezbollah guerrillas captured, Israel said
- An Israeli helicopter has crashed in northern Israel, killing two pilots. An army spokeswoman blamed technical problems, but Hezbollah reportedly claimed it had been shot down
- The UN launched an appeal for $150m (£81m) to help hundreds of thousands of displaced Lebanese civilians.
- US President George W Bush has ordered ships and helicopters to supply a "significant" amount of humanitarian aid to Lebanon from Tuesday, the White House said.
At least 372 Lebanese, the great majority civilians, have been killed during the conflict, which is now into its 13th day. Thirty-seven Israelis have been killed, about half of them civilians.
The Israeli offensive began after Hezbollah captured two Israeli soldiers in a cross-border raid on 12 July.
Ms Rice arrived in Beirut from Cyprus on a heavily armed military helicopter and went straight into talks with Mr Siniora.
"Thank you for your courage and your steadfastness," she told him, before the closed-door meeting. Afterwards she said she was "deeply concerned about the Lebanese people and what they are enduring".
She then met Shia parliament speaker Nabih Berri, who is said to have lines of communication with Syria and Hezbollah.
According to Lebanese government sources, Ms Rice made the release of the two Israeli soldiers and the withdrawal of Hezbollah forces from the border the pre-conditions for any ceasefire.
In Washington, White House spokesman Tony Snow said an immediate ceasefire was "unenforceable".
However in London, UK Prime Minister Tony Blair said what was happening in Lebanon was "a catastrophe" and that he hoped a plan for a ceasefire could be spelled out "in the next few days".
Mr Blair said a ceasefire plan would need the agreement of both sides to end hostilities, the return of the two Israeli soldiers and "some form of international force in the south in Lebanon".
For his part, Mr Olmert has said in a policy shift that Israel will be prepared to accept a European peacekeeping force providing it is robust and has a strong mandate.
In Brussels, EU foreign policy chief Javier Solana said several European countries were willing to contribute to such a force, which he said could be deployed under the umbrella of the UN Security Council.
UN Secretary General Kofi Annan said on Monday it was important that talks in Rome on Wednesday of Western and Middle Eastern ministerial powers succeeded.
He said it was vital that "we do not walk away empty-handed and dash the hopes of those caught in the conflict".
The BBC's Kim Ghattas, in Beirut, says Lebanon has felt let down by the international community because there has been no call for an unconditional ceasefire.
However, Mr Siniora has also said there will be no return to the status quo that existed before the violence started. And he insisted the Lebanese government was trying to extend its authority over the whole of the country.
An estimated 600,000 Lebanese have now been forced out of their homes.
Despite the diplomatic moves, Israeli Brig Gen Alon Friedman told Israel Army Radio the ground operation would probably go on for another 10 days.