A plume of smoke billows in the Lebanese border village of Aita al-Shaab after is was hit by Israeli artillery, Tuesday, Aug. 1, 2006

Heavy fighting was reported as Israeli troops battled Hezbollah guerrillas in border villages in southern Lebanon while Israeli Prime Minister Ehud Olmert insists his country is winning the battle against the Islamic militant group.     

Prime Minister Olmert struck a defiant tone, saying Israel is winning the battle against Hezbollah.

He said every extra day of fighting counts in diminishing the strength of the enemy. 

Ehud Olmert (file photo)

Speaking at a graduation ceremony at the National Security College, Prime Minister Olmert said Hezbollah would never again be able to threaten Israel.  He said it was not in Israel's interest to agree to a cease-fire right now.  But he also noted the beginning of a diplomatic process that would lead to an eventual cease-fire under different conditions than in the past.

Mr. Olmert's comments follow an approval by his security Cabinet to expand the ground offensive in southern Lebanon and shortly after the military said it would resume full-scale air strikes on Wednesday. 

Israel partially suspended air attacks for 48 hours in the wake of Sunday's bombing of the southern Lebanese village of Qana, in which nearly 60 people were killed, most of them women and children.

Despite a partial suspension, Israeli warplanes struck villages throughout much of southern Lebanon and targeted suspected Hezbollah strongholds elsewhere in the country.  And Israeli artillery bombarded border villages as ground forces expanded their operations in the area. 

Hezbollah's al-Manar television reported militants ambushed and pinned down Israeli troops in the village of Aita al Shaab, killing or wounding 35 soldiers.  Those casualties have not been independently confirmed.  Israel's justice minister, Haim Ramon, said about 300 Hezbollah fighters, have been killed since the conflict broke out nearly three-weeks ago while another minister put that figure at 400.  

The military says Israeli attacks have knocked out much of Hezbollah's rocket arsenal.  But Israeli Housing Minister Meir Sheetrit cautioned earlier that Israel cannot wipe out all of Hezbollah's rockets.

There is no such option, warned Sheetrit, not by land and not by air.  It is impossible to completely destroy their ability to launch Katyushas, the minister said.

International pressure for an immediate cease-fire is growing, but the United States and Israel remain firmly opposed to such a move, while other major powers within the European Union and the U.N. Security Council remain divided over the issue.