Peretz also said that Israel would accept a temporary international force, preferably headed by NATO, deployed along the Lebanese border to keep Hezbollah guerrillas away from Israel, according to officials in Peretz's office.
"The army's ground operation in Lebanon is focused on limited entrances, and we are not talking about an invasion of Lebanon. We are beginning to see the army's successes opposite Hezbollah," he told the Cabinet, according to a participant in the meeting.
"The army's goal is to create a new reality, mostly that Hezbollah won't be along the border," he said, adding that the army has found a lot of Hezbollah weapons during the operation.
Peretz also held a closed meeting with visiting German Foreign Minister Frank-Walter Steinmeier.
"Israel's goal is to see the Lebanese army deployed along the border with Israel, but we understand that we are taking about a weak army and that in the midterm period Israel will have to accept a multinational force," he said in that meeting, according to his office. Peretz suggested NATO be in charge of the force.
In other recent developments:
Warplanes on Sunday hit a minibus carrying Lebanese from border villages they were told by the Israeli military to flee, killing three and wounding 13, Lebanese security forces said. Hezbollah guerrillas fired rockets into northern Israel, killing at least two people.
Israeli troops continued to hold a Lebanese border village that they battled their way into the day before, but did not appear to be advancing, Lebanese security officials said. But warplanes and artillery were heavily battering areas across the south.
The minibus was carrying 16 people fleeing the village of Tairi, working their way through the mountains for the southern port city of Tyre. A missile hit the bus near the village of Yaatar, killing three and wounding the rest, security officials said. The wounded were taken to hospitals in Tyre.
On Saturday, the Israeli military told residents of Taire and 12 other nearby villages to evacuate by 4 p.m.
At least four other people were killed by strikes in the south, Lebanese television said but the deaths were not confirmed by security officials. About 45 people were wounded in Israeli air raids that targeted villages and towns around Tyre on Sunday, security and hospital officials said.
Haifa residents had stayed away from work since last week, when eight people were killed in a missile attack on a train maintenance depot in the city center. However, they were told they could return to work Sunday if their workplace had a secure bomb shelter.
Just before 11 a.m., air raid sirens shrieked throughout the city, followed by the explosions.
Police spokesman Avi Zelba said 13 rockets fell in the area, with most landing in open areas. One hit the house, while another struck a major road, rescue officials said.
Israel media also reported that a factory in Haifa was hit and several people inside were injured.
"My whole factory is totally ruined," owner David Tiboni told Israel Television.
Dolly Marom, 40, was in the basement of her building in Haifa's Nesher neighborhood when a rocket hit the building and blew the door open, causing her 12 and 13 year old children to burst out crying.
"It could kill us and that's it, and we did nothing to anyone," she said. "They're talking about the bombing in Beirut, they should see what happened in my house."
The three deaths in the minibus bring to at least 375 the official death toll provided by Lebanese authorities.
Israel's death toll stands at 36, with 17 people killed by Hezbollah rockets and 19 soldiers killed in fighting.