Fairuz Shahin is less than 2 days old, but she already embodies both the humanity and inhumanity of the war in Gaza, as well as its ironies and complexities.

She and her Palestinian mother were saved by Israeli doctors at a hospital that also treats wounded Israeli soldiers and which is directly threatened by Hamas rockets.

At the time of her birth, the Israeli military was relentlessly shelling Hamas targets in the Gaza Strip, killing or wounding hundreds of Palestinian children. Many of those injured children are treated by Fairuz's father, a paediatrician in Gaza.

“It's the absurdity of the Middle East,” said Lobel Ron, deputy medical director of Barzilai hospital in Ashkelon, an Israeli town ten miles (16km) north of Gaza. As he spoke, his wife called to say a Hamas bomb had just landed near their house.

Fairuz's mother, Manal Shahin, 33, is caught between gratitude to the Israeli doctors and fury at Israel's destruction of her homeland, between the joy of giving birth and fear for her family back in Gaza. She has been told that they have fled to a safer district, but she has been unable to speak to them for the past four days - not even to tell her husband of their daughter's birth.

“I feel anger, fear and uncertainty,” she told The Times as a siren warned of another incoming Hamas rocket. “May God finish this war as soon as possible so I can go home.”

For all her anxiety Mrs Shahin and her family are exceedingly lucky. Forty-five per cent of Gaza's population is aged 14 or under and children account for between a quarter and a third of the 700 Palestinians killed since the Israeli offensive began.

Israel has accused Hamas of using women and children as human shields, but Western NGOs in Gaza have said that is disingenuous. “The bottom line is if you're operating heavy weaponry in a very densely populated area, people who have nothing to do with the conflict will die. Sadly, this includes kids,” said Benedict Dempsey, of Save the Children.

Mrs Shahin's odyssey began three weeks ago when she brought her fourth and youngest child to Barzilai hospital. She was heavily pregnant but her 18-month-old son was suffering neurological problems and needed an MRI scan. She went to Ashkelon because Israel, as the occupying power, is legally responsible for giving Palestinians medical care they cannot get in their own territories.

Operation Cast Lead began while she was in Ashkelon and the border was shut off and she could not go home. On Tuesday morning she went into labour. There were serious complications, and that night doctors performed a urgent Caesarean section. Had she given birth in Gaza, where the hospitals are desperately short of equipment, medicines and power, she and Fairuz would almost certainly have died.

Looking pale and tired, Mrs Shahin posed for photographs with her 7.7lb baby yesterday and begged The Times to send some to her husband, Ahmed, so he could see his daughter.

Far from joyful, she said that she could scarcely sleep because she was so worried about him and her three other children - a boy and two girls, aged 11, 10, and 8. They live in Jabaliya, an eastern district of Gaza City that has been pounded by the bombardment. Indeed, The Times saw plumes of white smoke rising from the area later after hearing Israeli shells firing.

“It's a massacre. It's genocide. It's beyond imagination what's happening there,” Mrs Shahin said, adding that her husband was working around the clock at the Kamal Adwan hospital in Beitlahia, trying to save wounded children. “He doesn't stay at home. He's always in the emergency room.”

Asked whether Hamas had invited the destruction by raining rockets into southern Israel, she would say only: “Mothers and children don't interfere in politics. We just want to live in peace.”

More than 120 of those rockets have landed in Ashkelon since 2003. Earlier this week one killed a man and injured several others just outside the hospital. Last February another damaged the hospital's helipad.

Dr Ron recalled a Palestinian woman who had given birth to premature twins being evacuated to a bunker because of an incoming rocket. She told him that a few months earlier Hamas had fired rockets from her courtyard. “You can quite often see Palestinian patients lying side by side in the emergency room with people injured in Palestinian rocket attacks,” he said.

Dr Ron said that he and his staff had no objection to treating Palestinians. He said of Fairuz: “There must be people who believe we have delivered the next terrorist. I like to think we have delivered a future prime minister of Palestine who will bring peace to the area.”

Mrs Shahin said that Fairuz faced a bleak future in the impoverished, overcrowded Gaza Strip, with its rundown schools and desperate economy.

She said she did not want to raise another child in such dire conditions, but then she said: “Maybe, because she was born in Israel, she can become an ambassador of peace.”

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