The renewed diplomatic effort came after Israeli military officials announced on Tuesday that their army was now operating 8km inside southern Lebanon, where they were continuing to meet fierce resistance from Hezbollah fighters.
Fighters from the Shia militia killed four Israeli soldiers on Tuesday, hours after Israeli aircraft struck again in Beirut and across southern Lebanon.
Israeli missiles landed near a funeral procession in Ghaziyeh, a Shia town southeast of the port city of Sidon, scattering some of the 1,500 mourners in panic.
More missiles slammed into a building about five minutes after the procession passed.
One person was killed and five wounded in the attack, rescuers and witnesses said.
Mohammed Ghaddar, Ghaziyeh's mayor, said that 30 minutes later, Israeli warplanes staged four more bombing runs, destroying two buildings.
Twelve more people were killed and 18 wounded in the strikes, according to a tally from three area hospitals.
UN troops already in Lebanon have failed to keep the peace
Witnesses said one of the destroyed houses belonged to Sheikh Mustafa Khalifeh, a cleric linked to Hezbollah, but it was unclear if he was among the casualties.
Most Hezbollah officials have left their homes and offices since the offensive began nearly a month ago.
After the first strike, screams of "Allahu Akbar! [God is great]" rang out in the crowd marching with coffins. Some broke away from the procession, others continued on.
Hezbollah has continued to fire rockets at civilian areas of northern Israel.
Israel has said it will evacuate 15,000 civilians from areas hardest hit. More than 160 rockets landed in Israel on Monday, wounding several people.
More than 1,000 Lebanese – mostly civilians - are now thought to have died in the four-week conflict along with 99 Israelis, including 63 soldiers.
The number of Hezbollah fighters killed is not known and it is not clear if they are included in the total Lebanese death toll.
In New York, representatives from the United Nations security council, together with Israeli, Lebanese and Arab diplomats, have continued to search for a solution to the conflict.
Amid the diplomatic wrangling, the US and France appear to be persuading other countries to support an international peacekeeping force.
From his ranch in Texas, George Bush, the US president, outlined his plan to deploy an UN-backed international force.
"As these Lebanese and international forces deploy, the Israeli Defence Forces [Israeli army] will withdraw and both Israel and Lebanon will respect the Blue Line that divides them," Bush said on Monday.
Israel's military toll continues to
rise as the war grinds on
However, diplomats are struggling to bridge the massive gulf between the Israeli and Lebanese demands.
Fouad Siniora, Lebanon's prime minister, has said that Israel should withdraw from all of south Lebanon even before an international force arrives. Israel says that it will not withdraw until Hezbollah stops firing rockets.
Lebanon has already rejected one draft resolution because it did not call for an immediate withdrawal of Israeli forces. A final version of the resolution is expected to be approved on Wednesday.
On Tuesday Israeli military officials announced that the Israeli army was now holding land up to 8km inside Lebanon.
This claim has been confirmed by Hezbollah, which reported heavy fighting near the village of Dabel.
Amir Peretz, Israel's defence minister, told the Israeli cabinet that he might expand operations up to the Litani river, which is 30km north of the border.
He told MPs on Tuesday that he had instructed all military commanders "to prepare for an operation aimed at taking over launching areas [to] reduce as much as possible Hezbollah's rocket launching capability".
"If we see that the diplomatic efforts do not yield the results we expect, we will have to do it ourselves."
In Lebanon’s southern port city of Tyre, Israeli aircraft dropped leaflets warning people that any vehicle moving south of the Litani would be attacked, Aljazeera said.
The leaflets also repeated earlier calls for the city's residents to leave the city. Tyre is 8km south of the Litani river. Israeli aircraft have already cut roads and bridges leading to the city.
Lebanon's cabinet voted on Monday to deploy 15,000 of its own troops to try and stop the fighting.
On Tuesday morning it was reported to have begun calling up reservists.
Ghazi al-Aridi, the Lebanese information minister, said the Lebanese army did not intend to remove Hezbollah from the area.
Lebanese soldiers could soon find
themselves on the frontlines
Instead, he said, the Shia Muslim group would be allowed to remain there "as a party that represents an entire segment of the population".
The decision was supported by Hezbollah's two cabinet members.
Ehud Olmert, the Israeli prime minister, said Lebanon's offer to deploy troops was "an interesting step".
"We are studying the proposals. We do not want to occupy Lebanon. We do not want to stay in Lebanon. We want to apply the goals of the operation - to prevent rocket fire and to push Hezbollah from the region," he said.
The Lebanese army has not formally taken part in the fighting, although dozens of its soldiers have been killed after their barracks and positions have been hit by Israeli bombs.
Individual army units have also fired on Israeli aircraft flying over Lebanon.