Israeli ground troops are battling Hezbollah guerrillas near the Lebanese border town of Bint Jbail, while Israeli warplanes are continuing to hit targets across Lebanon.
Lebanese security officials say at least seven people were killed in an overnight missile strike on a house in the town of Nabatiyeh, north of Tyre. They say it was not immediately clear why the house was targeted.
Israeli military officials say two Israeli soldiers died and at least 13 others were wounded in battles Monday. They say several Hezbollah fighters were also killed, but no confirmed figure was available.
Also on Monday, an Israeli military helicopter crashed in northern Israel, killing two crew members. The cause of the crash is under investigation.
Guerrillas also fired more rockets into northern Israel, injuring at least eight people, but there were no fatalities.
Meanwhile, the U.N. humanitarian chief criticized Hezbollah for what he called the "cowardly blending" among Lebanese civilians in the face of Israeli offensive.
Speaking to reporters after a visit to Beirut, Jan Egeland said he heard Hezbollah guerrillas were proud because they had lost few fighters since civilians were bearing the brunt of the conflict.
Egeland has also called Israel's military offensive "a violation of international law."
Israel began its offensive against Hezbollah after guerrillas captured two Israeli soldiers, triggering a battle that killed eight Israelis. The violence has claimed the lives of more than 370 Lebanese, almost all civilians, and 37 Israelis. About 20 Israeli troops have died in the fighting.