A UN-brokered ceasefire to end the month-long war between Israel and Hezbollah guerrillas formally took effect on Monday, but no immediate confirmation was available that it was being observed.
Israel launched new air strikes on Lebanon just before the truce deadline, Lebanese security sources said.
Earlier, Israel's Haaretz newspaper reported on its website Prime Minister Ehud Olmert had told his army to observe a truce from 2 am on Monday and to start withdrawing some of its estimated 30,000 troops in south Lebanon.
But Israeli air strikes went on well after that time, targeting areas in eastern Lebanon and near the southern city of Sidon, the security sources said. Fierce clashes between Israeli troops and Hezbollah were also reported early on Monday.
Air strikes on the village of Brital near Lebanon's eastern border with Syria overnight killed at least nine civilians, medics said. One person was killed in a strike on a Palestinian refugee camp, the security sources said.
On Sunday, Israel's cabinet approved a UN Security Council resolution to end the fighting and deploy a United Nations force of up to 15,000 troops to help enforce the truce. The Lebanese government and Hezbollah have also agreed to the resolution.
Both Israel and Hezbollah, however, have said they would respond to any violation of the truce by the other side.
"It will be a fragile truce," said a Western diplomat.
Hezbollah launched its heaviest one-day rocket barrage on Israel on Sunday since the start of the war. Israeli security officials said more than 250 rockets were fired, killing a man and wounding about 90 people. The port city of Haifa was hit.
Around 1,100 people in Lebanon, mostly civilians, and 154 Israelis, including 114 soldiers, have been killed in the war, which was triggered when Hezbollah captured two Israeli soldiers in a cross-border raid on July 12.
Israeli officials said the Jewish state believed it would be entitled under the UN resolution to use force to prevent Hezbollah from rearming and to clear guerrilla positions out of southern Lebanon after the truce took effect.
Senior Foreign Ministry official Gideon Meir said his country would not violate the truce.
"If Hezbollah continues to fire rockets or shoots at our soldiers then we will have to respond. There will not be a violation from our side," he said.
Western diplomats and UN officials said they feared Israel's broad definition of "defensive" actions could lead to a resurgence in large-scale fighting and prevent the swift deployment of the UN troops, likely to be led by France.
Hezbollah has said its guerrillas would observe a truce once it began but reserved the right to fight Israeli soldiers still on Lebanese soil.
Israeli Foreign Minister Tzipi Livni repeated Israel's position that its troops would pull out from southern Lebanon only when the UN force arrived. The United Nations has said the deployment could take up to 10 days.
EU foreign policy chief Javier Solana, who has been helping coordinate European contributions to the UN force, said he would like to see international troops start deploying to southern Lebanon this week or early next week.
"I've been speaking to several countries during the day and night and I think we will be able to guarantee that the force, as far as the Europeans are concerned, will be robust," he said.
Besides France contributing troops, Italy says it is ready to dispatch up to 3,000. Portugal, Finland and Spain are also considering deployments. Solana listed Australia, Canada, Malaysia and Indonesia as non-EU nations prepared to help.
The deployment of the Lebanese army in the south is another key part of the UN resolution adopted on Friday.
The Israeli army said around 530 Hezbollah guerrillas had been killed during the war. Hezbollah has acknowledged only a few score dead.
The Haaretz newspaper reported the Israeli government was willing to discuss a possible release of Lebanese prisoners in exchange for the freeing of the two captured Israeli soldiers.
The war in Lebanon coincided with an Israeli offensive in the Gaza Strip to free another captured soldier.
More than 170 Palestinians, more than half of them civilians, have been killed in the military campaign in Gaza.