NEW YORK (CNN) -- With hopes dimming for a quick end to fighting in Lebanon, Israeli Deputy Prime Minister Shimon Peres presented five conditions Monday that he said must be met before Israel can achieve peace with Hezbollah.
"There must be a change in the whole situation in the Middle East," Peres said. "There must be a sustainable peace, a more profound arrangement that will answer the real problems."
In a briefing with reporters at the Omni Berkshire Place hotel in Manhattan, Peres said Israel must:
- ensure that Hezbollah will never return to the Israeli-Lebanese border;
- obtain the release of two Israeli soldiers captured by Hezbollah guerrillas July 12;
- stop Hezbollah from shooting missiles and rockets into Israel;
- prevent the Lebanon-based militant group from rearming with missiles and rockets from Syria and Iran; and
- free Lebanon from Hezbollah's control.
Israel doesn't have a problem with Lebanon, but with Hezbollah and its Syrian and Iranian backers, he said.
"Though Hezbollah is a Lebanese body, they don't serve any Lebanese purpose," he said, adding that the militants are trying to make Israel's northern neighbor "part of the sphere of influence of Iran."
Peres said that Iran intended to acquire nuclear weapons as well as remake the Middle East.
"That becomes a real problem for the rest of the world" he added, saying Iran's actions will prompt other countries to follow suit and increase the odds that such weapons end up in terrorists' hands.
Peres made no apologies for Israel's attacks on Lebanon since Hezbollah guerrillas seized the two Israeli soldiers 20 days ago in a cross-border raid.
"We shall fight because we were attacked," he said. "We didn't initiate the fight, nor can we ignore it."
Israel faces mounting international pressure to halt its campaign, especially after an airstrike Sunday killed at least 54 civilians in the southern Lebanese town of Qana.
Israel called the Qana attack a tragic mistake and announced it would temporarily halt its airstrikes.
But bombing continued Monday in southern Lebanon, and Israeli Prime Minister Ehud Olmert said there would be no cease-fire "in the coming days."
Regarding the Qana attack, Peres said, "In war, you have a lot of mistakes. The greatest mistake is the war itself. Anyone who wants to prevent mistakes must stop the war."
He added that Israel was carrying out an investigation to determine how the bombs used in the attack landed more than 300 meters (328 yards) from their intended target.
"We are still investigating what happened. That does not prevent us from feeling deeply sorry to see children losing their lives," he said.
Still, he said, "When you use civilian life as a shield for rockets and missiles, according to international law, you have the right to defend yourself."
Israeli airstrikes and artillery have pounded Lebanon for almost three weeks, leaving nearly 500 people dead. Hezbollah has fired scores of rockets daily into northern Israel, killing at least 18 Israeli civilians.
Clashes with Hezbollah have left 33 Israeli troops dead. Hezbollah's casualties are unknown.
Regarding criticism that Israel's response to Hezbollah has been disproportionate, Peres pointed out that militants fire 100 missiles and rockets every night into northern Israel.
"We don't feel that this is exactly proportionate," he said. "If somebody would suggest another method on how to stop it, we would be happy."
Peres said that the captured Israeli soldiers are "alive and healthy" and that Israel holds Lebanon responsible for their safety.
"Lebanon cannot behave like they are responsible for nothing and the whole world owes them everything," he said.
At 83, Peres said he has lived through wars and "terrible times" when people thought Israel would be destroyed.
"All those times, I remained an optimist and a man of peace," he said. "I didn't change my mind. We shall make it."