Rockets from militants are slamming into Israeli cities, Israeli air strikes are killing Palestinian children, and no end is in sight

The yellowing skin on the boy's face was pocked with black marks from the blast. A tuft of wiry black hair had escaped from the shroud in which his body was bound; his eyelids were closed, his lips slightly parted. He had been dead for two hours but still no one knew his name.

Then one man drew back from the crowd jostling around the body on the mortuary tray in the Kamal Adwan hospital in Beit Lahiya, having identified his 15-year-old nephew Nayif Qarmout, whom his family had last seen heading off to school on Monday. "We don't know what happened," the uncle said, blinking with shock.

A few miles away, in the Shifa hospital in Gaza City, Nayif's injured schoolmates had some clues. Three were in surgery, with injuries ranging from moderate to critical. But a pair of shivering teenage brothers, Hani and Mo'aed Qanou', blood dripping from shrapnel wounds, had given an account to their mother. The boys had set off for school but spotted some militants running away after firing a rocket. They went to investigate the launcher – perhaps out of simple teenage curiosity, perhaps to see if there was something they could salvage for sale. Then an explosion killed Nayif and injured five others. Israel denied it had carried out an air strike.

Nayif was one of 23 Palestinians killed since Friday in an escalating round of attack and counter-attack between militants in Gaza and the Israeli military.

A senior Egyptian security official said on Monday night that Israel and militant factions in Gaza had agreed to an Egyptian-mediated truce to end the violence.

The official told Reuters that both sides "agreed to end the current operations" including an unusual undertaking by Israel to "stop assassinations" in a deal expected to take effect at 1am local time.

However, Israel or the Palestinian factions would not comment on whether a deal had been struck.

Five civilians – two teenage boys, two men in their 60s and a woman aged 30 – are among the Gaza dead, since Israel assassinated a militant leader in order, it says, to prevent an attack aimed at its citizens. Israel has carried out dozens of air strikes, with booms regularly punctuating the constant buzz of aerial drones across northern Gaza.

Palestinian militants have fired more than 150 rockets into Israel, some reaching the cities of Ashdod and Be'er Sheva. Schools in the south were closed for a second day as families crowded into bomb shelters in response to sirens. Buildings and cars were damaged, and residents treated for shock and minor injuries. Israel has deployed its costly Iron Dome defence system around 70 times, with an 80% success rate. Terri Millstone, 57, a teacher who lives in Ashdod, said the past few days had been horrifying. "People are afraid to open stores, to walk on the street. Everyone is looking for the nearest shelter," she said. "The rockets are coming indiscriminately. I've lived through a few rounds in Ashdod, but this round is really scaring me."

There had been three alerts on Monday morning, the last just before she boarded a bus for another town. "The bus driver just drove like a lunatic and we all said a prayer," Millstone said.

Attempts to broker a ceasefire appeared to founder on the insistence of Islamic Jihad, the main group firing rockets, that Israel end targeted assassinations. But a military spokesman, Brigadier-General Yoav Mordechai, told Israel Radio: "If the fire ends, the Israel Defence Forces will not continue [air strikes], but the IDF will continue thwarting any attempted terrorist attacks."

Hamas's leader, Mahmoud al-Zahar, said he expected the violence to calm down, denying to Reuters that Hamas had taken any decision to escalate. "Hamas is trying to reach a truce conditioned on the Israeli enemy halting the aggression and pledging that targeting will not happen again," he said from Cairo.

But Taher Nounou, a Hamas spokesman in Gaza City, told the Guardian: "We didn't participate up to now, but I don't know if this situation will continue. If [Israel] goes on we can't stand by and do nothing while our people are killed. We don't want to make an escalation, but maybe we have no choice." Hamas had conveyed this message to Israel, he said.

Ban Ki-moon, the UN secretary general, said he was "gravely concerned at the latest escalation … and once again civilians are paying a terrible price". Rocket attacks on Israeli civilians were "unacceptable", he said, but Israel should "exercise maximum restraint".

His words meant little to Adila Useila, the mother of 13-year-old Ayoub, who was killed on Sunday just 30 metres from his home, in Jabalia, on his way to an extra tuition class. Clutching Ayoub's shredded school bag amid a crowd of mourners, Useila, 44, said Ayyoub her son had been torn apart in the blast, and not all of his body parts had been recovered. The mother of 13 claimed no rockets had been fired from the area before the air strike. "How did the drones not see my son's school bag?" she asked. "They see everything on the ground."

Ayoub, whom she described as a quiet and helpful boy, was the second son she had lost; another, a militant, was killed three years ago, aged 22.

Before leaving home on Sunday morning, Ayoub had asked for money to buy a mother's day present, she said, adding: "I ask all Palestinian resistance movements to fire rockets, to target Israeli schools. This would be the best Mother's Day gift for me."