Fouad Siniora urged the UN to supervise a truce to end Israeli raids that have killed more than 80 Lebanese.
The Arab League added to calls for the UN to act - its secretary general said the Middle East peace process was dead.
Meanwhile Hezbollah launched rockets at Tiberias in the deepest such attack on Israel. Four Israelis were injured.
The conflict has also dominated the G8 summit in Russia whose president called for "maximum effort" to defuse tension.
Mr Siniora asked all Lebanese to be united and stand behind their government.
He said his government knew nothing of Hezbollah's border raid that captured the two Israeli soldiers and left eight more dead last Wednesday.
Mr Siniora called the Israeli operation a "murderous machine" but said Lebanon would prevail.
He added: "Lebanon is a disaster zone... and [it] pleads to its friends in the world to rush to its aid."
Israel expanded its bombardment on Saturday, attacking a large number of targets across the country.
Warplanes fired rockets on the Lebanon-Syrian border and hit the centre of Beirut for the first time.
Eighteen Lebanese civilians, including women and children, were killed on the coastal road to the southern city of Tyre when their vehicles were struck by missiles as they fled a village.
Hezbollah's offices in Beirut were destroyed. The group injured four Israelis in cross-border rocket attacks on Tiberias.
Israel has deployed Patriot interceptor missiles in the northern port city of Haifa which was hit by rockets earlier.
It also warned Lebanon not to fire on Israeli aircraft.
"Israel has avoided harming the Lebanese army until now, but Israel will not hesitate to strike at any party that operates against it," a military spokeswoman said.
In Cairo, Arab foreign ministers holding an emergency conference blamed the current outbreak of violence on the failure of the Middle East peace process.
Secretary General Amr Moussa said the process was dead.
The final resolution of the meeting called for an immediate ceasefire and a plan to take the Arab-Israeli conflict back to the UN Security Council.
At the G8 summit in St Petersburg, Russian President Vladimir Putin called for the world to make the "maximum effort" to defuse tension.
He condemned "terrorist acts that involve kidnapping people".
But he added: "We have the impression that, besides rescuing the servicemen who have been abducted, Israel is pursuing other, wider objectives."
US President George W Bush put the blame squarely on Hezbollah and said Syria should act to curb the group's operations.
In other Israeli attacks on Saturday:
- Warplanes struck the northern port city of Tripoli and carried out raids in north and north-eastern Lebanon for the first time
The Israeli Army said any responsibility for endangering the civilian population rested with Hezbollah.
Thousands of foreigners are leaving Beirut, leaving its economy in tatters.
Countries including the US and France are making plans to evacuate their nationals from Lebanon.