The war in Gaza erupted afresh on Monday as Israel warned of a protracted military campaign to destroy cross-border tunnels and disarm Hamas and other militant groups.

"We need to be prepared for a long operation until our mission is accomplished," Israeli prime minister Binyamin Netanyahu said in a televised press conference, rejecting mounting international calls for an immediate and unconditional ceasefire.

Just after midnight , reports from Gaza described flares lighting up the sky amid intense shelling, with drones flying overhead. Gaza's interior ministry announced that the house of a Hamas leader, Ismail Haniyeh, was hit by a missile. No immediate casualties were reported.

Netanyahu – who described the conflict as a "just war" – spoke after a series of dramatic events following a lull in fighting on Sunday and early Monday. Eight children playing in a park in a Gaza refugee camp were killed, the main public hospital was struck, four Israeli soldiers were killed in a mortar attack and militants from Gaza infiltrated Israel through a tunnel.

Israel Defence Forces warned residents of neighbourhoods in northern Gaza – including Shujai'iya, the scene of some of the most intense fighting in the three-week war – to evacuate immediately, suggesting a major escalation of military action was imminent.

Benny Gantz, Israel's military chief of staff, and defence minister Moshe Ya'alon also said the operation would continue as long as necessary. "Gaza residents should distance themselves from areas in which Hamas is acting because we will get there and it will be painful," Gantz said.

The renewed bloodshed added urgency to international calls for a ceasefire. Earlier on Monday the UN secretary-general, Ban Ki-moon, reiterated the security council's call for an immediate and unconditional ceasefire, demanding that both sides end the fighting "in the name of humanity".

The statements from the three men directing the military offensive on Gaza will gratify hawkish cabinet ministers and media commentators who have been stridently urging an expansion of the operation to try to deal a decisive blow to Hamas.

But Israel's decision to press ahead with the operation risks alienating its key ally, the US, after Barack Obama told Netanyahu of his concern over civilian casualties.

Eight children and two adults were killed, and dozens more injured, at the seafront Shati refugee camp on Monday. At the same time the Shifa hospital in Gaza City was hit. The incidents followed the end of a 24-hour unilateral ceasefire declared by Hamas to mark the start of the Muslim holiday of Eid.

Israel categorically denied its forces were responsible for the strike on the hospital or the camp, saying rockets launched by militants had misfired. But medical staff and other witnesses insisted missiles were fired at the hospital from an F-16 jet. Israel has previously accused Hamas militants of hiding in the hospital premises."We have not fired on the hospital or on Shati refugee camp," Major Arye Shalicar told AFP. "We know that Hamas was firing from both areas and the missiles struck these places."

In southern Israel a Palestinian mortar strike from Gaza killed four soldiers, the IDF said. A fifth soldier was killed in southern Gaza, bringing total military casualties to 48. A number of others were wounded in the attack. It was not confirmed whether the victims were military personnel or civilians.

At least one militant among a group which infiltrated Israel through a tunnel was killed as the men emerged near a community close to the border. Hamas said 10 Israeli soldiers had lost their lives but there was no confirmation from Israel.Warning sirens were reported in northern Israel, including the city of Haifa, suggesting Hamas could be deploying long-range missiles in its arsenal.

Earlier, following the end of the ceasefire at 2pm, there was renewed rocket fire from Gaza. The IDF warned that it would respond to rocket fire with further air strikes. "The IDF is free to attack after any fire if there is any," Brig Gen Motti Almoz told Israel Radio.

In New York Ban accused Netanyahu and Hamas leader-in-exile Khaled Mishal of being morally wrong for allowing civilians to be killed.

He urged both sides to demonstrate political will and compassionate leadership to end the bloodshed.

Gaza was in a "critical condition" after three weeks of military offensive, which raised serious questions about proportionality, he told reporters.

The UN and Obama had also called for an immediate and unconditional ceasefire. The calls followed a series of unilateral ceasefire announcements by both sides, each of which was rejected by the other amid mutual blame and recrimination.

A presidential statement issued by the UN security council just after midnight in New York on Sunday, called on the parties to the conflict "to accept and fully implement the humanitarian ceasefire into the Eid period and beyond" and "to engage in efforts to achieve a durable and fully respected ceasefire, based on the Egyptian initiative".

It noted "grave concern regarding the deterioration in the situation as a result of the crisis related to Gaza and the loss of civilian lives and casualties" and called for Israel and Hamas to respect international law.

Obama told Netanyahu of his concern at the rising number of civilian deaths and urged an immediate, unconditional ceasefire. He stressed the importance of "ensuring Israel's security, protecting civilians, alleviating Gaza's humanitarian crisis and enacting a sustainable ceasefire that both allows Palestinians in Gaza to lead normal lives and addresses Gaza's long-term development and economic needs, while strengthening the Palestinian Authority".

However, in his television address on Monday night, Netanyahu vowed: "We will not end this operation without neutralising the tunnels whose sole purpose is killing our citizens."

According to the UN, more than 20 hospitals and medical centres have been hit by Israeli shelling and about 1,060 people – mostly civilians – killed, with 6,000 injured. The Israeli death toll exceeded 50.

In Egypt, former president Mohamed Morsi who was overthrown in a military coup a year ago praised the "resistance" in Gaza.

"Our compass is set on supporting Palestine against the usurping occupier and we are with any resistance against any occupier," Morsi said in a message posted on his official Facebook page. "A full salute to those who resist and to the revolutionaries."

Hamas is an offshoot of Egypt's Muslim Brotherhood, which has been outlawed under the regime of Abdel Fatah al-Sisi.