US President George W Bush has said he suspects that Syria is trying to use the crisis in the Middle East to reassert its influence in Lebanon.
The human cost of the crisis has continued to mount
He suggested that Hezbollah activities were being orchestrated by Damascus.
Israel attacked Lebanon after the militant group captured two soldiers in a cross-border raid on 12 July.
Overnight air strikes are reported to have killed dozens of people, with 20 people reported dead in the southern village of Srifa.
Casualties were also reported in raids near Nabatiyeh in the south and Baalbek in the east.
Israel air strikes also targeted Hezbollah positions in the capital Beirut.
Early in the morning, Israeli troops crossed into southern Lebanon to carry out what the army called "restricted pinpoint attacks".
About 230 Lebanese people have died in the week-long conflict, most of them civilians. Twenty-five Israelis have died, including 13 civilians killed by Hezbollah rocket attacks.
President Bush said Hezbollah was the "root cause" of the current crisis.
"Syria is trying to get back into Lebanon, it looks like to me," Mr Bush said.
"And there is suspicion that the instability created by the Hezbollah attacks will cause some in Lebanon to invite Syria back in."
He reiterated his stance that Israel had a right to defend itself, but said Israel had been asked to be "mindful" of the new Lebanese government of Prime Minister Fouad Siniora.
"It's very important that this government in Lebanon succeed and survive," he said.
The BBC's Jonathan Beale in Washington says the US strategy is becoming clearer - to turn international attention and anger away from Israel's actions, and to focus on those of Hezbollah and Syria instead.
But he adds that some will question the evidence of blatant Syrian interference in Lebanon.
With no sign of an end to the violence, many thousands of people continue to flee Lebanon.
Several countries have sent ships and helicopters to move their nationals from Lebanon, while tens of thousands of people - including many Lebanese families - have fled across the land border to Syria.
Aid agencies fear 500,000 people have been displaced within Lebanon itself - and have called for a ceasefire to allow humanitarian relief work to start.
Diplomatic efforts continue, with European Union foreign policy chief Javier Solana due to hold talks with Israeli Foreign Minister Tzipi Livni, as well as Palestinian officials and Egyptian mediators.
A UN team that has been in the region over the past few days is preparing to fly back to New York to brief Secretary-General Kofi Annan, who is due to address the Security Council on Thursday about the crisis.
On Tuesday, Israeli Prime Minister Ehud Olmert told Israeli diplomats that Hezbollah's capture of their soldiers had been co-ordinated by Iran.
It was, he said, timed to coincide with the G8 summit in Russia and deflect attention away from Iran's nuclear programme.