Condoleezza Rice, the US Secretary of State, paid a surprise visit to bombed-out Beirut today to kick off a diplomatic mission to resolve the crisis in the Middle East.

But even as she landed in Lebanon, en route to Jerusalem, Israeli armoured units were embroiled in their fiercest clashes yet with Hezbollah guerrillas along the country's southern borders.

Ten Israeli soldiers were reported to have been wounded in fighting near the southern Lebanese village of Maroun al-Ras, which the Israelis captured at the weekend.

The Arabic-language television channel al-Jazeera said that two others had been killed when an Israeli helicopter crashed near the border. Hezbollah claimed to have brought down the helicopter although Stephen Farrell, a Times correspondent who visited the scene, said that it appeared to have hit a power line and pylon.

Dr Rice spent two hours with Fouad Siniora, the Lebanese Prime Minister, before a series of meetings with other Government officials.

But it was far from clear what her trip was expected to achieve given that Israel has said that it could not accept any cessation of hostilities until its military objectives are satisfied, including clearing Hezbollah positions in southern Lebanon.

A senior commander on Israel's northern front, Brigadier-General Alon Friedman, said that the ground operation would continue for up to ten days. "The scope continues to grow in recent days," he told Israel Army Radio. "We are advancing."

Dr Rice told reporters on her plane from Washington that although the United States considered a ceasefire to be an urgent priority, any agreement had to remove the long-term threat posed by Hezbollah to Israel.

"It is very important to establish conditions under which a ceasefire can take place. We believe that a ceasefire is urgent," she said. "It is important to have conditions that will make it also sustainable."

In London, Tony Blair said that some kind of plan to end the conflict, based on the return of two abducted Israeli soldiers and the deployment of an international force in a buffer zone in southern Lebanon, might emerge in the next few days.

"There have been as you might expect over the past few days enormous diplomatic efforts to get us to the point where I hope at some point within the next few days we can say very clearly what our plan is to bring about an immediate cessation of hostilities," the Prime Minister said after talks with Nouri al-Maliki, his Iraqi counterpart.

The US Secretary of State left Washington last night and landed at Larnaca airport in Cyprus, before changing to a helicopter for the short flight to Lebanese capital - the same trip, in reverse, taken by thousands of foreigners evacuated from the city by sea.

Almost 400 people, the vast majority civilians, have been killed in Israeli air strikes and bombardment and 37 Israelis have also been killed, mostly by Hezbollah rocket attacks on northern Israel.

Dr Rice is due to travel on to Jerusalem later today, for talks with Ehud Olmert, the Prime Minister, and to meet Mahmoud Abbas, the Palestinian President, before an international conference on the Lebanese crisis in Rome on Wednesday.

So far, "pinpoint" incursions against Hezbollah positions has failed to reduce the level of cross-border rocket fire into northern Israel that has claimed the lives of around 25 people. Hassan Nasrallah, the Hezbollah chief, said that Israel’s assaults would not stop cross-border rocket fire - one of Israel's state objectives for the offensive. Israeli officials said that 95 rockets hit Israel yesterday.

"Any Israeli incursion will not have political results unless it achieves any of the announced goals, most importantly to stop the bombardment of Zionist settlements ... and I assure you that this goal will not be achieved," Mr Nasrallah told Lebanon’s As-Safir daily.

More Israeli troops crossed into Lebanon at daybreak today and took control of a hilltop on the outskirts of Bint Jbail, a Hezbollah stronghold, although without capturing the town itself. An Israeli artillery barrage left plumes of grey smoke rising over the area.

There was no confirmation from Israel of the casualties although it said that in overnight fighting its troops had captured two Hezbollah guerrillas, the first in 12 days of attacks on Lebanon.

In a fierce battle at the weekend, Israeli ground forces took control of Maroun al-Ras, a hilltop town and Hezbollah stronghold east of Bint Jbail, the military said.

An overnight break in Israel’s airstrikes on Lebanon ended when Israeli jets attacked targets in southern Lebanon, the official National News Agency reported.

Arab diplomats say that both Egypt and Saudi Arabia are pushing Syria to end its support for the Hezbollah guerrillas, which could weaken Hezbollah and make it more amenable to a ceasefire. The group is, however, also backed by Iran.

The US Secretary of State, under pressure from Western allies to end the costly Israeli offensive, said that the United States’ poor relationship with Syria had been overstated and indicated an openness to working with Damascus to resolve the crisis.

Meanwhile foreigners continued to be evacuated from Lebanon by sea. The European Union was sending a ship to the southern port of Tyre and the Canadian Government is to send another ship in tomorrow to pick up foreigners who have been unable to leave by land to Syria because the Israeli airstrikes have destroyed bridges and highways.

Some 4,500 British citizens and 12,000 Americans have left Lebanon, and the evacuation appears to be nearing completion.

Israel has not yet defined safe corridors for refugees in Lebanon, but it has allowed ships carrying humanitarian aid to dock in Beirut port. An Italian warship brought food, medicine, tents, blankets, water, electrical generators and ambulances. A ferry carrying supplies from France also arrived. Lebanese aid officials say however that what has arrived is completely inadequate.

The UN's top humanitarian official, Jan Egeland, said that he would be calling for at least $100 million in immediate aid for Lebanon. Billions of dollars would be needed to repair the damage to Lebanese infrastructure, newly rebuilt after emerging from years of civil war, he said.

Mr Egeland yesterday toured the rubble of Beirut’s bombed-out southern suburbs, a once teeming Shia Muslim district where Hezbollah had its headquarters. He condemned civilian casualties on both sides but called Israel’s offensive "disproportionate" and "a violation of international humanitarian law".