The death toll, if confirmed, could be the worst for Israel since fighting, prompted by Hezbollah's kidnapping of two Israeli soldiers and the killing of eight others, broke out two weeks ago, the Reuters news service reported.
"Our men can hear the screams of their wounded calling for help," one Hezbollah fighter was quoted as saying.
The Jerusalem Post reported 30 Israeli soldiers had been wounded in the fighting, three seriously, but could not confirm the deaths.
No Hezbollah casualties were reported, but Israeli security forces estimate 130 Hezbollah fighters have died by Tuesday, Reuters reported.
Israel has been eager to secure the town of Bint Jbail, 2.5 miles from the Israeli-Lebanon border, according to reports from senior Israeli officers, Reuters reported. The town has been identified as an Hezbollah stronghold.
Wednesday's fighting broke out when Israeli troops tried to take the main entrance to the town after four days of advancing, Lebanese security sources told the Associated Press.
The fighting in the town of 30,000 came as Israel and Hezbollah traded separate air strikes along the border. Israeli jets launched more than 50 air strikes in southern Lebanon, according to reports. Hezbollah launched around 119 rockets into Israel, wounding 55 Israelis, the Jerusalem Post reported.
About 1,400 rockets have been fired into Israel since fighting broke out 15 days ago, the newspaper reported. Nineteen civilians have died as a result and more than 1,200 have been wounded.
An estimated 422 Lebanese civilians have died, and more than 750,000 have been driven from their homes, according to the Associated Press.
Israeli Prime Minister Ehud Olmert has called for the establishment of a "security zone" along the southern Lebanon border manned by international forces that would be free of Hezbollah fighters.
A U.N. force currently patrols the border, but has been unable to stop the violence, the AP said.
The latest violence in cross border attacks came a day after four U.N. observers died in an Israeli bombardment of their observation post in the southern Lebanese town of Khiam.
Olmert expressed "deep regret" for the deaths, but rebuffed a charge by the U.N. that the attack was deliberate, the AP reported.
"It's inconceivable for the U.N. to define an error as an apparently deliberate action," Olmert said.
Twelve U.N. officials have been killed or injured in direct hits on U.N. outposts over the last two weeks, the international organization said.
An angry U.N. Secretary-General Kofi Annan said he had received personal assurances that the Khiam position and other clearly marked U.N. outposts would be safe from Israeli aerial attacks.
On Wednesday, workers pulled the bodies of three of the observers from the rubble. A fourth still was buried. The observers were from China, Austria, Canada and Finland, according to the AP.