The fighting took place in the Bint Jubeil area, north of Maroun al-Ras, and involved aerial and ground forces.
The Israel Defense Forces has called Maroun al-Ras its first foothold in southern Lebanon as it tries to create a security buffer zone and stop militants from firing rockets.
The IDF believes Bint Jubeil is an important weapons storage area for Hezbollah, with tunnels, bunkers and caves holding large supplies of missiles, rockets, and launchers, military sources told CNN.
“There are large numbers of explosive devices and mines in the area, and heavy fire is being exchanged,” said IDF spokeswoman Miri Regev.
“We intend to clean out the area in order to avoid firing at Israel. We intend to reach the central towns from which Katyushas [rockets] are being fired, dismantle terror infrastructure, to hit the terrorists and then to leave.”
The IDF said Monday it had seized two Hezbollah guerrillas “suspected in involvement in terror activities” in Maroun al-Ras. The guerrillas were taken into custody Sunday and are being held in Israel.
The Israeli military also said one of its helicopters crashed Monday on the Israeli side of the Lebanon border close to Bint Jubeil.
The IDF labeled the crash an accident and said there were casualties. Also Monday, Israeli police said 90 rockets had been fired at Israel as of 3 p.m. (10 a.m. ET) wounding seven people.
The latest barrage of Hezbollah rockets landed near the northern Israeli cities of Tiberias, Kiryat Shmona, Maalot, Nahariya and north of Haifa.
Red Cross: Israeli missile strikes ambulances
Meanwhile, Israeli bombs hit buildings and cars in Maaliye, south of Tyre, and Israeli forces struck a truck in Kfarshima, southeast of Beirut, near the main airport, Lebanese security forces said.
The Israeli air force struck a site east of Sidon, Lebanon, used by Hezbollah to launch rockets, and a car filled with Hezbollah militants who were fleeing from the area after launching rockets, an IDF spokesman said.
An Israeli missile hit two Red Cross ambulances parked in the southern Lebanese town of Qana, killing one person and seriously wounding two others late Sunday, according to a Red Cross official.
The Red Cross official in Tyre told CNN that the ambulances, clearly marked as Red Cross vehicles, were part of an effort to transport people wounded in the town of Tibneen to hospitals 20 miles to the west in Tyre.
Israeli officials have said they do not intend to carry out a full-scale ground invasion in Lebanon but will continue pinpoint attacks on specific targets.
Meanwhile, U.S. Secretary of State Condoleezza Rice made an unannounced stop Monday in Beirut to meet with Lebanese Prime Minister Fouad Siniora as the crisis entered its 13th day.
Israeli artillery and warplanes have been pounding Lebanon since July 12, when Hezbollah kidnapped two Israeli soldiers in a cross-border raid.
Hezbollah has responded to the bombardment by firing hundreds of rockets into northern Israel.
More than 60 Hezbollah rockets hit northern Israel on Sunday, killing two civilians and wounding more than 20 others, military officials and police said.
Lebanese authorities reported Monday that 275 people have died and 727 have been wounded since the conflict began.
Israel said 17 civilians and 20 soldiers have died and more than 300 civilians and more than 60 soldiers have been wounded.