JERUSALEM, Jan 5 (Reuters) - People in Gaza were in dire need of food and medical supplies, aid agencies said on Monday, but Israel's ground assault and air raids were hampering relief efforts.

Freezing cold is compounding the misery of children caught in the conflict. And body bags for victims are in short supply.

"The situation in Gaza since the Israel Defense Forces launched their ground offensive on Saturday night has become both chaotic and extremely dangerous," the International Committee of the Red Cross said in a situation report.

Air raids had damaged hospitals, water supply systems, government buildings and mosques but it was difficult for ICRC staff to move around to assist, it said.

About 530 Palestinians have been killed, at least a quarter of them civilians, since Israel launched its offensive on Dec. 27 to curtail Hamas rocket attacks from Gaza.

Ground troops invaded the enclave, home to 1.5 million Palestinians, on Saturday night after a week of bombardments from the air and from naval vessels.

Hospitals were inundated with Palestinian wounded, the ICRC said. Fresh supplies were urgently needed, including painkillers and anaesthetics but also body bags and sheets to wrap corpses.

The hospitals were relying on generators for electricity because of damage to the main power system but they can break down at any time.

An ICRC surgical team was due to move into Gaza on Monday to help surgeons after waiting for several days in Jerusalem for permission from Israeli authorities.

"We are seriously concerned about the reports we are receiving with regard to civilian casualties and damage to civilian objects," said Pierre Wettach, ICRC chief for Israel and the Palestinian territories.

Work on the ground was also perilous for medics. Three paramedics and three volunteers have been killed so far and planes have bombed the Health Care Union in Gaza City and destroyed four ambulances, Palestinian medical officials said.

The Palestinian Red Crescent said the combat had prevented ambulance staff from responding to many calls.

On Sunday, a pregnant woman in Zeitoun in northern Gaza had to be taken to hospital on a donkey cart but did not make it in time. The baby was stillborn and she suffered a ruptured uterus.

Save the Children staff began to deliver food aid to families on Sunday but air assaults and ground fighting made it dangerous for staff, the agency said in a statement.

"The situation has reached a critical level for children who are exposed to and experiencing violence, fear and uncertainty," Save the Children emergency team leader Annie Foster said.

Some families fear to leave their houses while others are being forced to flee them.

The winter cold was also a danger to children as electricity cuts have mean many homes lack heating.

"Families must leave windows open at night so that they will not be broken by percussive shocks or flying debris from the ongoing bombardment. This means that children, the majority of them poor and malnourished, are essentially spending the night exposed to the elements," Foster said.

Israel has accused Hamas of sheltering among the civilian population and using sites such as mosques and schools as military posts. It has allowed some convoys of trucks with food and fuel to enter the blockaded enclave.

At least three children were among a dozen Palestinian civilians killed on Monday. Since the fighting began, 59 children have been killed, Palestinian health officials say.