Israeli soldiers are fighting Hezbollah militants inside the Lebanese border, Israeli military officials say.
The UN says almost a third of the dead and wounded are children
The clashes come as Israel keeps up its bombing of Lebanon, carrying out 80 air strikes early on Thursday.
Lebanon's president has called for an immediate ceasefire, calling Israel's offensive - which has killed 300 people and displaced 500,000 - a "massacre".
Bombed roads are hampering aid efforts, with the UN warning the humanitarian crisis is worsening by the hour.
The nine days of fighting - triggered by the capture of two Israeli soldiers by the militant Hezbollah group in a cross-border raid - have left 29 Israelis dead, including 15 civilians killed by rockets fired by Hezbollah into Israel.
US troops land
Captain Eric Schneider from the Israeli Defence Force told the BBC there was heavy fighting between Israeli troops and Hezbollah militants in two places inside Lebanon's border.
Hezbollah issued a statement saying that it had destroyed two Israeli tanks. The Israeli army has not confirmed this, but did say at least three Israeli soldiers had been injured.
The Israeli public security minister, Avi Dichter, said Hezbollah had to understand that its "time is up" and that Israel will only accept a Lebanese government force at the border.
During the current crisis, Hezbollah's missiles have penetrated as far south as the cities of Haifa and Tiberias.
Many thousands of people continue to flee Lebanon, and a number of countries have sent ships and helicopters to move their nationals.
Britons in the Lebanese capital, Beirut, are being transferred to HMS Bulwark, which can carry 5,000 people, while about 40 US marines from the USS Nashville have come ashore in Beirut to assist with the evacuation of US citizens.
It is the first time US troops have been in Lebanon since Hezbollah militants blew up a marine barracks in Beirut in 1983, killing 241 personnel.
In other developments:
- Cyprus says it cannot cope with the influx of evacuees, expected to reach 60,000, and appeals to the European Commission for additional planes to fly evacuees to their home countries
- The UN High Commissioner for Human Rights, Louise Arbour, warns that those involved in the spiral of violence between Israel and Lebanon could face war crimes charges if they are found to have deliberately attacked civilians
- UN Secretary General Kofi Annan and US Secretary of State Condoleezza Rice are to discuss the crisis on Thursday
- Pope Benedict XVI calls for a day of prayer on Sunday for an immediate ceasefire in the crisis
But as thousands of foreigners leave, aid agencies are expressing increasing concern for those who will be left behind, especially people in the south who have been displaced by the fighting.
In an interview with French radio, Lebanese President Emile Lahoud called for an immediate truce to end what he described as a "massacre".
"Israel is bombing everything, even little streets, even ambulances, even lorries which are taking the food supplies," Mr Lahoud said.
Mr Lahoud appealed for an instant end to the violence saying, "after that we can talk. We can discuss everything, but first the fighting has to stop".
Civilians caught up
The United Nations' emergency relief co-ordinator, Jan Egeland, said that without a truce allowing aid agencies to begin the relief effort there would be a "catastrophe".
"It is nearly impossible in southern Lebanon to move anything anywhere because it is too dangerous," he said.
FOREIGNERS IN LEBANON
Sri Lanka: 80,000
UK: 22,000 (inc. 10,000 with dual nationality)
Figures correct at start of conflict
Mr Egeland said that neither Hezbollah nor the Israelis seemed to care about civilian suffering, adding that nearly a third of the dead or wounded were children and the wounded could not be helped because roads and bridges had been cut by Israeli air strikes.
"The Israeli military attacks are all over the country. There are aerial bombardments which are in hundreds of places really. I think it is a disproportionate response, really," Mr Egeland told the BBC.
"But I also clearly see that Hezbollah is trying to blend into the civilian population in too many places and they bear also a heavy responsibility for this. They do not seem to care that they really inflict a lot of suffering on their own population," he added.
In the southern Lebanese city of Tyre the evacuation of hundreds of foreign nationals who had been trapped by the fighting has begun.
Foreigners trapped in the city of Tyre are now being evacuated
The group, which was forced to spend the night in the open on the beachfront after the evacuation was cancelled on Wednesday, are being transferred in UN convoys to Tyre port then ferried to an awaiting passenger ship.
Many Lebanese fear that the violence could escalate further once the foreign nationals are evacuated.
"I have a very bad feeling that after the foreigners flee the bombings will get worse," Beirut resident Ziad Nayef told Reuters. "Nobody cares about Arab lives."
The Israelis say they are fighting to end the control of Hezbollah over the lives of ordinary people on both sides of the border.
Israeli Prime Minister Ehud Olmert said the campaign against the militants would continue "as long as necessary" to free its captured soldiers and ensure Hezbollah is not a threat.