Palestinian medical sources say the number of people killed in Gaza now stands at more than 500, with some 2,500 wounded. These figures cannot be independently verified.
Five Israelis have been killed since the start of Israel's military operation, which is now in its 10th day.
Speaking to MPs, Mr Barak said the offensive would continue until "peace and tranquillity" was secured for Israeli civilians, referring to Israeli towns that have come under rocket attack by militants.
Speaking on Hamas-run al-Aqsa TV, Mahmoud Zahhar praised those fighting for Hamas and hinted that Palestinian militants would try to target more Israeli civilians.
Palestinian militants fired 20 missiles into southern Israel on Monday, the Israeli army said.
Israeli sources say about 4,000 infantry are inside Gaza, backed by tanks.
International journalists are still not allowed inside the Gaza Strip to verify reports of troop movements or casualties.
However, the BBC's Mike Sergeant, in Jerusalem, says that for now, the ground operation - which began late on Saturday - seems to be focused on areas in northern Gaza.
One million people are without electricity. Crucially the hospitals in Gaza are running on emergency generators - this in my book amounts to a humanitarian crisis
Israeli troops have been fighting Hamas militants around Beit Hanoun and Jabaliya. Gaza city itself - a little further south - has been encircled.
As yet, Israeli tanks and heavy armour do not appear to have entered the most densely-populated areas, our correspondent says.
The Palestinian health ministry says 90 people have been killed in Gaza since the ground operation began. Reports say casualties are continuing to pour into the territory's overstretched hospitals.
One resident of a refugee camp in the Gaza beach area, Abu Aisha, told the BBC he lost several members of his family in an Israeli attack.
"The attack resulted in the death of my brother, his two wives and four children.
"We took out three bodies and the rest we could not find. There are four or five bodies under the rubble, and we cannot take them out."
For the people of Gaza, living conditions are deteriorating sharply. Supplies of fuel, food, water, and wheat are said to be running desperately low.
Reports from the Israeli and Egyptian sides of the Gaza boundary
A spokesman for Unrwa, the UN aid agency for the Palestinians, said food was urgently needed and people were facing "serious hunger", with supplies for just 48 hours.
"One million people are without electricity. Crucially the hospitals in Gaza are running on emergency generators. This in my book amounts to a humanitarian crisis," Christopher Gunness told the BBC.
Israel said it had allowed a convoy of 80 lorries carrying food and medicines through Gaza's southern frontier.
Away from the frontline, diplomatic efforts to halt the fighting in the Gaza Strip are moving into high gear.
French President Nicolas Sarkozy will be shuttling across the Middle East, taking in Egypt - which mediated a recent six-month truce between Hamas and Israel - as well as Jerusalem, the West Bank and Syria.
On Monday morning an EU delegation met Egyptian President Hosni Mubarak in the Red Sea resort of Sharm el-Sheikh.
Afterwards a spokesman for French Foreign Minister Bernard Kouchner told the BBC that Europe wanted the fighting to stop now.
"We need and we ask for an immediate ceasefire, which is mainly first a humanitarian truce, which we hope will lead to a durable ceasefire in order to restart the political discussions," said Eric Chevalier.
"The impact on the civilian population is absolutely disastrous and we need, and the people of the region need, an immediate ceasefire."
But Ms Livni said Israel was aiming to "change the equation in the region".
"When Israel is being targeted, Israel is going to retaliate," she said.
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