Israel continued its assault on a variety of targets in Gaza Monday as European foreign ministers and French President Nicolas Sarkozy worked to secure a ceasefire.

But with Palestinian rocket fire still being launched, Israel said it won't stop its punishing offensive until "peace and tranquility" are achieved in southern Israeli towns.

Israel, which is attacking Gaza by air, sea and with troops on the ground, seized control of high-rise buildings Monday and destroyed houses, mosques and smuggling tunnels.

According to Palestinian health official Dr. Moaiya Hassanain, about 20 Palestinian children were killed Monday, the 10th day of the Israeli offensive.

Since Israel launched its air offensive on Dec. 27, Gaza health officials report 550 people have been killed, of which 200 were civilians. About 2,500 have been wounded.

Five Israeli civilians and one soldier have also been killed by militants.

CTV's Middle East Bureau Chief Janis Mackey Frayer said Israel has managed to bisect the Gaza Strip, severing the main north-south corridor.

"The rationale to this is that it may impede the ability of Hamas and other militants to move around -- to be able to have rocket squads on the move," Mackey Frayer reported Monday from the region.

Inside Gaza, Palestinian-Canadian Nizar Kaddah said Monday he's living in fear and cannot leave his home.

"Even if I want to go and get some food or some bread, I cannot get out of my house," Kaddah told CTV's Canada AM on Monday.

"I'm afraid that if I drive my car a rocket or something will hit my car."

Kaddah, who is in Gaza with his wife and two children, said he's tried to call the Canadian embassy in Ramallah but has been unable to get through.

Hamas leader Mahmoud Zahar called Monday for Palestinians to fight back against Israeli troops and to keep targeting Israeli civilians.

"The Zionists have legitimized the killing of their children by killing our children. They have legitimized the killing of their people all over the world by killing our people," Zahar, in a rare appearance, said in a video broadcast on Hamas TV.

Meanwhile, Abu Obeida, a spokesman for Hamas' military wing, warned Israeli forces that militants "wait for you in every street and every alleyway."

Israeli Defense Minister Ehud Barak said Monday the attacks would not stop until Israelis in the south, who have been targeted by constant Palestinian rocket fire, can live in "peace and tranquility."

Diplomatic efforts

The U.S. State Department said Washington was pressing for a cease-fire that would include a halt to rocket attacks -- and an arrangement for reopening crossing points on the border with Israel. State Department spokesman Sean McCormack said another element would address the tunnels into Gaza from Egypt, through which Hamas has smuggled materials and arms.

But the deputy head of Hamas' politburo in Syria rejected the U.S. proposal. Moussa Abu Marzouk, told the Associated Press the U.S. plan would impose "a de facto situation" and encourages Israel to keep attacking Gaza.

French President Nicolas Sarkozy visited the region Monday in an attempt to broker a truce and encourage the resumption of peace talks. Europe "wants a cease-fire as quickly as possible," Sarkozy said after meeting Palestinian President Mahmoud Abbas. He urged Israel to halt the offensive, while blaming Hamas for acting "irresponsibly and unpardonably."

Meanwhile, a European Union delegation met with Foreign Minister Tzipi Livni.

"The EU insists on a cease-fire at the earliest possible moment," said Karel Schwarzenberg, the foreign minister of the Czech Republic, which took over the EU's presidency last week from France. Schwarzenberg added that rocket attacks on Israel also must stop.

Earlier Monday, Livni met with her counterparts from France, Sweden and the Czech Republic but still rejected calls for an immediate halt of the offensive.

Livni told reporters Monday that Israel's incursion was a form of "legitimate self-defence," according to Israeli daily Haaretz.

"Israel wants very much for any sort of lull in this campaign to be drafted on its terms," Mackey Frayer said.

She said although Israel is demanding a complete end to Palestinian rocket fire it would be "naive" to think that every single rocket is going to stop.

"What is likely to happen is that Israel would want to see at least a diminished capability on the part of Hamas and its ability to fire rockets," Mackey Frayer said.

"But we are witnessing what is the heaviest military offensive by Israel into the Gaza Strip in the last number of decades and Hamas is still firing rockets -- some with longer range -- into Israeli towns."

Rex Brynen, a professor of political science at McGill University, said Monday the problem for Israel will be finding an exit strategy if Hamas doesn't agree to give up.

"I think the current dynamic is a very dangerous and difficult one," Brynen told CTV Newsnet from Montreal.

"I certainly don't imagine that we're going to have any breakthroughs any time soon in the peace process but there have also been conflicts far, far bloodier than the Arab-Israeli conflict that have ended in peace."

With files from The Associated Press