Israeli Prime Minister Benjamin Netanyahu said on Sunday he expected to complete a new Gaza offensive "fairly quickly" as the UN Security Council heard new demands for an end to suffering in the Palestinian enclave.

Netanyahu, speaking after his security cabinet on Friday approved a much-criticised plan to take control of Gaza City said he had no choice but to "complete the job" and defeat Hamas to free hostages seized from Israel.

Gaza City, the enclave's most populous centre, came under Israeli air strikes late on Sunday and at least five people were killed at a sandwich shop in the Sabra neighbourhood, health officials at Shifa Hospital said.

Palestinian media said two Al Jazeera journalists were also killed when a missile hit their tent near the hospital, and tank fire was reported in the area.

Netanyahu's office said late Sunday the prime minister had spoken with US President Donald Trump about "Israel's plans to take control of the remaining Hamas strongholds in Gaza."

Earlier in the day, the Israeli leader said the new Gaza offensive aimed to tackle two remaining Hamas strongholds in what he called his only option because of the Palestinian group's refusal to lay down its arms.

Hamas says it will not disarm unless an independent Palestinian state is established.

It was not clear when the offensive, which would be the latest in successive attempts by the Israeli military to clear the militants from Gaza City, would begin.

"The timeline that we set for the action is fairly quickly. We want, first of all, to enable safe zones to be established so the civilian population of Gaza City can move out," he added.

The city, home to a million people before the two-year-old war, would be moved into "safe zones", he said. Palestinians say these have not protected them from Israeli fire in the past.

Israel's military chief has voiced opposition to occupying the entire Gaza Strip and has warned that expanding the offensive could endanger the lives of hostages Hamas is still holding and draw its troops into protracted and deadly guerrilla warfare.

Netanyahu said his goal was not to occupy Gaza. "We want a security belt right next to our border, but we don't want to stay in Gaza. That's not our purpose," he said.

European representatives at the United Nations said famine was unfolding in Gaza and Israel's plan would only make things worse.

"Expanding military operations will only endanger the lives of all civilians in Gaza, including the remaining hostages, and result in further unnecessary suffering," Denmark, France, Greece, Slovenia and the United Kingdom said in a joint statement.

"This is a manmade crisis, and therefore urgent action is needed to halt starvation and to surge aid into Gaza," they said.

Malnutrition is widespread in the enclave due to what international aid agencies say is a deliberate plan by Israel to restrict aid. Israel rejects that allegation, blaming Hamas for the hunger among Palestinians and saying a lot of aid has been distributed.

Five more people, including two children, died of malnutrition and starvation in Gaza in the past 24 hours, Gaza's health ministry said, taking the number of deaths from such causes to 217, including 100 children. (Reuters)