By Nidal al-Mughrabi

GAZA (Reuters) -As Israel prepared on Sunday for a ground assault on the Hamas-controlled Gaza Strip, Palestinians who have lost family members in air strikes were bracing for more destruction.

Um Mohammad Al-Laham's 4-year-old granddaughter Fulla Al-Laham lay in a Gaza hospital. She said an Israeli air strike hit the family home, killing 14 people including Fulla's parents, siblings and members of her extended family.

"All of a sudden and without warning, they bombed the house on top of the residents inside. No-one survived except my grandchild Fulla," said the grandmother, who has witnessed many wars between Hamas and the Israeli army over the years.

She says this is the toughest.

"Fourteen people martyred, no-one was left except Fulla," she said. "She doesn't talk, nothing, just lays in her bed and they give medicine."

One other 4-year-old child in the family had also been left with almost no relatives, the grandmother said.

Israel has unleashed the heaviest air strikes ever on Gaza.

It has vowed to annihilate the Palestinian militant group Hamas in retaliation for a rampage by its fighters in Israeli towns eight days ago in which its militants shot men, women and children and seized hostages in the worst attack on civilians in the country's history.

Some 1,300 people were killed in the surprise onslaught, with graphic mobile phone video footage and reports from medical and emergency services of atrocities in the overrun towns and kibbutzes.

Israel has put Gaza, home to 2.3 million Palestinians, under siege and told people to leave their homes in the north of the enclave and move south.

Hamas has urged people not to leave, saying roads out are unsafe.

The United Nations says so many people cannot be safely moved within Gaza without causing a humanitarian disaster.

THE ROAD SOUTH

Some residents said they would not leave, remembering the "Nakba," or "catastrophe," of 1948 when many Palestinians were forced from their homes during the war that accompanied Israel's creation.

Gaza authorities said more than 2,300 people have been killed, a quarter of them children, and nearly 10,000 wounded.

Rescue workers searched for survivors of air raids.

In Khan Younis, southern Gaza, Mohamed Abo Dakka said his family was still under the rubble after an Israeli strike.

"I lost my son, my cousins, and the whole family," he said. "I didn't lose them because they were arrested for fighting on the front lines... we were just at home, sitting at home.

"We can't find equipment to search and pull them out."

The expected Israeli ground offensive and the air strikes have raised fears of unprecedented suffering in the narrow, impoverished enclave, one of the most crowded places in the world.

At Gaza's Kamal Edwan Hospital, where some children were attached to ventilators, Dr Hussam Abu Safiya, said: "If you want to kill us, kill us while we continue working here, we will not leave. We need days and weeks to secure another place."

"The situation is really dangerous," he said. "Transferring these children from this place means handing them a death sentence. They will die and this equipment only operates with electricity and oxygen."

Hospitals say they are running out of medicine and fuel under the Israeli blockade.

Witnesses in Gaza City told Reuters the Israeli offensive had forced more people from their homes, some seeking shelter at medical facilities. Gaza's largest Shifa hospital was overcrowded.

"We are living the worst nightmare of our lives. Even here in the hospital we are not safe. An air strike hit in the area outside the hospital around dawn," said a 35-year-old woman who declined to give her name.

Taking the road to southern Gaza has become more difficult as several people who made the journey say Israel continues to bomb around it. The Israeli military was not immediately available for comment.

Ashraf Al-Qidra, Gaza's health ministry spokesman, said 70% of people in Gaza City and the north of the strip are deprived of health services after the Palestinian refugee agency UNRWA evacuated its headquarters and suspended its services.

East of Khan Younis in southern Gaza, where hundreds of northern residents have fled to, some locals cooked for displaced people, using firewood to prepare 1,500 meals of meat and rice donated by residents.

"We are running out of gas, so we are cooking on firewood," said Youssef Abu Assi, one resident helping out.

(Additional reporting by Abed Saleh, Ismail Khader, Muath Freij; Writing by Michael Georgy; Editing by Hugh Lawson and Janet Lawrence)