Israeli warplanes have struck at suspected Hezbollah sites in Sidon and the capital Beirut.
Families have been fleeing Israeli strikes in southern Lebanon
In Sidon, 14 people were injured and a mosque was destroyed in the first strikes on the southern port city.
The UN's humanitarian chief Jan Egeland has been touring shattered districts of Beirut, and said the devastation was "a violation of humanitarian law".
Meanwhile, at least two people have died after Hezbollah militants launched rockets at the Israeli city of Haifa.
A volley of explosions on Sunday set sirens wailing and emergency services racing through the streets, says the BBC's Raffi Berg in Haifa, on Israel's northern coast.
Reports say at least one car travelling on a main road in Haifa was hit, and a house was badly damaged.
An hour after the first volley of explosions, a second huge blast shook the city.
'Block after block'
Mr Egeland arrived in southern Beirut on Sunday just hours after Israeli strikes on the Hezbollah stronghold, and the ruins of high-rise apartment blocks were still smouldering.
Mr Egeland expressed shock that "block after block" of buildings had been levelled.
"It makes it a violation of humanitarian law," he said.
Mr Egeland appealed for both sides to put a halt to attacks, and urged Israel to allow the secure passage of aid.
Amid growing concerns about the hundreds of thousands of civilians displaced by the bombing, Israel has eased some restrictions on Lebanon's blockaded ports to allow aid into the country.
Envoys to press Israel
Three European envoys are to hold talks with Israel on Sunday, ahead of a visit by the US Secretary of State.
Israel has urged the US to hasten the delivery of weapons
Israeli officials are scheduled to meet German Foreign Minister Frank-Walter Steinmeier and French Foreign Minister Philippe Douste-Blazy, who has warned of a spiral of violence.
UK Foreign Office Minister Kim Howells will also travel to Israel for talks, having already accused its government of imposing a collective punishment on Lebanon in its 12-day campaign against Hezbollah fighters.
And US Secretary of State Condoleezza Rice is travelling to the Middle East on Sunday.
Along with southern Beirut and Sidon, there were Israeli bomb attacks on the Bekaa valley and explosions were heard near the southern city of Tyre on Sunday.
Israel says its forces have driven Hezbollah guerrillas out of the hilltop village of Maroun al-Ras close to the Israel border, where six Israeli commandos were killed earlier this week.
The report has not been confirmed independently and Hezbollah's al-Manar TV station reported earlier on Saturday that fighting was under way in the village.
There are substantial numbers of Israeli forces near the border, and military sources suggest that there will be continued incursions in the coming days.
Israel insists it has no plans for a large-scale invasion and its ground forces are only entering Lebanon to destroy Hezbollah hideouts that cannot be attacked from the air.
Israel had warned residents in 14 villages in a swathe of southern Lebanon to leave by Saturday evening.
The BBC's Martin Asser in the southern city of Tyre described long queues of taxis and cars negotiating bomb-cratered roads and making detours around destroyed bridges.
Many civilians from villages in the region had gathered in the city during the week and are now trying to leave. However, many people say they are reluctant to move without UN protection.
The New York Times daily has cited US officials saying the US is rushing a delivery of satellite and laser-guided bombs to Israel.
The latest crisis was triggered by the capture of two Israeli soldiers by Hezbollah militants on 12 July.
More than 350 Lebanese have been killed in the 11 days of violence, many of them civilians, and angry protests condemning Israeli attacks have been held in cities around the world.
At least 36 Israelis have been killed, including 17 civilians killed by rockets fired by Hezbollah into Israel.