Israel immediately responded with five artillery shells into Lebanon, calling it a "pinpoint response at the source of fire".
Correspondents say this is a dangerous moment in the current conflict.
The rocket attacks from Lebanon have raised concerns about a wider war in the region, says the BBC's Middle East Editor Jeremy Bowen.
But the Lebanese Prime Minister Fouad Siniora was swift to condemn the attack, and called for the army and the UN to investigate.
Information Minister Tarek Mitri told the AFP news agency he had been "assured" by the militant group Hezbollah they were not involved in the rocket attacks.
Israeli cabinet minister Raif Eitan said he believed Palestinians in Lebanon, not Hezbollah, were behind the attack.
On Wednesday, Hezbollah leader Hassan Nasrallah spoke openly about the possibility of a renewed conflict with Israel, saying its fighters were on high alert along the Lebanese-Israeli border.
Northern Israel came under attack from rockets fired by Hezbollah during the brief war with Lebanon in the summer of 2006.
In Gaza, Israel continued its offensive overnight with 60 airstrikes targeting police sites, 10 Hamas tunnels, weapons storage facilities, launching pads "and a number of armed gunmen", the Israeli army said.
Naval and artillery units "continued to support the ground forces" with one soldier lightly wounded, the army added.
Shopping for 'basic needs' in Gaza market
The bombardment followed a three-hour pause in fighting on Wednesday to allow vital humanitarian aid into Gaza.
Aid agencies report that Gazans rushed into the streets to buy essential supplies and visit relatives in hospital during the lull.
But the traditionally neutral ICRC accused Israel of failing to honour its obligations under international law to treat and evacuate the wounded in Gaza.
It said the Israeli military was in the neighbourhood and must have been aware of the incident involving the four starving children but did nothing to help.
"Neither did they make it possible for us or the Palestinian Red Crescent to assist the wounded," the ICRC's Pierre Wettach said.
About 700 Palestinian and 11 Israeli lives are said to have been lost since the offensive began 12 days ago.
Casualty claims in Gaza have been difficult to independently verify.
While the BBC has had Palestinian producers reporting from Gaza, Israel only allowed Western TV crews to enter on Wednesday, embedded with its army.
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