Calgary-based Marwan Diab, who is visiting Gaza City with his wife and four children, said he wants to get his family out of the territory as soon as possible. (CBC)

At least 36 of 58 Canadians known to be in the Gaza Strip have asked for assistance to leave the territory as Israel escalated its attack on the Hamas militant group with a ground offensive over the weekend, but the earliest they could leave would be Monday, Israeli officials said.

The Canadian government said Sunday that it asked Israeli authorities Friday to issue the necessary travel permits to allow Canadians to leave Gaza as quickly as possible, the CBC's Nahlah Ayed reported.

But Israeli officials said the request only came Saturday evening, the same night that the ground offensive began, killing 64 Palestinians. At least 512 Palestinians and five Israelis have died since Israel launched its campaign in Gaza on Dec. 27.

Among those who want to leave the territory is Marwan Diab of Calgary, who was visiting Gaza City with his wife and four children.

"I want to get them out as soon as possible," he told CBC News. "You cannot imagine the amount of violence that is happening, the magnitude of this wave of violence."

Wafa Zakout, who returned to Gaza City to sell her house and move to Toronto, said she hasn't slept properly for almost a week.

"I am so nervous … because of the situation," she said.

Israeli officials said Sunday the first opportunity for Canadians to leave the territory would be Monday, but there were no guarantees the border crossings would be open.

"We are only targeting Hamas objectives and should they take the main road to the crossing, the army is informed of their movement and no harm should come to them anyway," added Yigal Palmor, a spokesman with the Israeli foreign ministry.