BEIRUT, Lebanon (CNN) -- Israeli special forces battled Hezbollah guerrillas Thursday during a second day of fierce ground fighting in war-ravaged southern Lebanon.
The Israeli offensive began is intended to wipe out the remaining capabilities of the Islamic militia, Israeli military officials said.
The Israeli military estimates that its air assault on Lebanon has destroyed about half of Hezbollah's military strength. It is using ground forces to target Hezbollah's remaining artillery, believed hidden in caves, tunnels and basements.
CNN cannot independently confirm Israel's estimation of Hezbollah's military strength.
As Israel and Hezbollah stepped up their assaults, U.N. Secretary-General Kofi Annan on Thursday demanded "an immediate cessation of hostilities" to prevent further loss of life, allow for humanitarian relief and give diplomacy a chance.
While Israel "has a right to defend itself" against Hezbollah attacks on its cities and soldiers, "the excessive use of force is to be condemned," Annan said in an address to the U.N. Security Council.
Annan also condemned Hezbollah for starting the crisis and for holding "an entire nation hostage." (Full story)
The fighting began after Hezbollah guerillas captured two Israeli soldiers during a raid into northern Israel on July 12.