Fuad Siniora said: "The country has been torn to shreds. Can the international community stand by while such callous retribution by the state of Israel is inflicted on us?
"You want to support the government of Lebanon? Let me tell you ... no government can survive on the ruins of a nation.
"I hope you will not let us down. We the Lebanese want life. We have chosen life. We refuse to die."
Wednesday's death toll reached 74, as Israeli strikes killed 72 people in Lebanon and a Hezbollah rocket attack left two Arab-Israeli children dead in the northern Israeli town of Nazareth.
More than 300 people have now been killed and 500,000 displaced during the week-long conflict.
Jets dropped bombs on an area of southern Beirut where Israeli commanders said senior Hezbollah leaders were sheltering.
Israeli military officials said dozens of aircrafts dropped 23 tonnes of explosives on what they described as a bunker in the Bourj al-Barajneh section of southern Beirut.
Three unusally heavy explosions were heard in the evening from the southern districts of the capital.
An army spokesman said Hezbollah's leader, Sheikh Hassan Nasrallah, may have been hiding at the site.
Hezbollah said none of its leaders was killed during the air strike.
A statement from the group said: "Hezbollah denies that any of its leaders or personnel were killed during the latest bombardment ... in the southern suburb."
The statement said that the bombed building was a mosque under construction and not a bunker housing Hezbollah leaders.
Wave of attacks
Throughout Wednesday, Israel pressed on with a wave of attacks from air and sea against southern and eastern Lebanon, flattening houses, destroying roads and hitting trucks, police said.
Twenty-five people were killed and 26 wounded in one village where residents said 10 houses were reduced to rubble by shelling from Israeli gunboats and aircraft.
Eleven other civilians were killed in an Israeli air strike on a four-storey building in the eastern Lebanese village of Nabi Sheet.
Israeli helicopters also fired rockets at a residential Christian district in Beirut, the first direct strikes in the centre of the capital, raising concerns about the evacuation operation under way at the nearby port.
Condoleezza Rice, the US secretary of state, and Javier Solana, the EU foreign policy chief, were to meet Kofi Annan, the UN secretary-general, in New York on Thursday.
Annan has proposed the creation of an international force to restore calm in Lebanon.
Solana said: "We will work very, very hard to see if we can have an end of hostilities and the beginning of something of a political nature before the end of next week."