Crucial Lebanese cabinet talks on disarming Hezbollah fighters in southern Lebanon under a UN-brokered ceasefire have been put off.
The port city of Tyre saw heavy Israeli bombardment on Sunday
A truce between Israel and Hezbollah is due to come into force at 0500 GMT.
The postponement, amid reported divisions, seriously complicates the establishment of a stable ceasefire, the BBC's Nick Childs in Beirut says.
Israeli Prime Minister Ehud Olmert ordered the country's army to halt fighting at 2300 GMT on Sunday.
Israel will now begin withdrawing some of its forces immediately, according to the newspaper Haaretz, reporting on a meeting between Mr Olmert, Defence Minister Amir Peretz and senior army staff.
But some Israeli troops will remain in southern Lebanon to hand over to an international force.
"You can't move from black to white easily - there will be a period of gray, " said Major General Benny Gantz, the head of Israel's ground forces.
Mark Malloch Brown, the UN's Deputy Secretary General, said it might take a month before a joint UN-Lebanese force was fully in place.
"It's going to be weeks, not days and may even, before you hit the full total, be a month or so," he told the BBC's Have Your Say programme.
An unrelenting barrage of rockets and shells from both sides of the border on Sunday suggest that Israel and Hezbollah will continue to attack each other until the deadline, the BBC's Adam Mynott reports.
The Israeli military intensified their assault, determined to try to achieve a military success at the eleventh hour, our correspondent says.
Lebanon's cabinet indefinitely postponed its meeting.
After five hours of discussions on Saturday, it had agreed to accept a UN Security Council ceasefire resolution with reservations.
The second gathering was meant to consider the details of implementation.
However, the issue of Hezbollah's disarmament and its military presence in southern Lebanon continues to cause major tensions within the fragile government, our correspondent reports.
He says that without a meeting and an agreed plan, it seems that the deployment of 15,000 Lebanese army troops to the south is unlikely to go ahead.
Even if the planned ceasefire happens, the prospects of continuing skirmishes on the ground will remain high, he adds.
Hezbollah, a member of the government, says it will abide by the resolution but retains the right to continue attacks until the last Israeli soldier has left Lebanese soil.
Crescendo of violence
At least 19 Lebanese people, including a mother and her three children, were killed in Israeli attacks on Sunday, Lebanese officials said.
David Grossman's son Uri was killed in fighting on 12 August
Israeli emergency services reported that a Hezbollah rocket - one of some 250 fired during the day - had killed a civilian in northern Israel.
And the Israeli military said that five of its soldiers had died in fighting on Sunday.
The son of David Grossman, a well-known Israeli novelist and peace activist, was killed on Saturday while serving in Lebanon.
Staff Sgt Uri Grossman, 20, was killed by an anti-tank missile just days after his father joined an appeal by leading Israeli intellectuals for an end to the war.
Sunday's Israeli assault saw warplanes bomb petrol stations in Tyre, sending up thick clouds of smoke.
The BBC's Jim Muir described a crescendo of violence in the hills near the city as shells, bombs and rockets smashed into their targets.
And the sound of huge explosions reverberated across Beirut as the Israeli air force carried out a new raid on southern districts of the city.
Rescue workers said that several multi-storey buildings had collapsed.
News also came in of air strikes on targets in eastern Lebanon late on Sunday.
Hezbollah rockets hit Yaara in northern Israel, killing the civilian, and Haifa's city centre and suburbs also came under bombardment.
Earlier, Israel's cabinet voted 24-0 with one abstention to accept the UN resolution.
More than 1,000 Lebanese have been killed in the conflict since Hezbollah militants captured two Israeli soldiers on 12 July in a cross-border raid. Israel's official death toll stood at 163 on Sunday, including 43 civilians.