Bloodshed in and around Gaza surged Tuesday with strikes killing 13 Palestinians, a day after five Israeli soldiers died, shattering hopes for an end to three weeks of violence.

It was a bloody start to the three-day Muslim holiday of Eid al-Fitr which began on Monday, with international demands for an end to the fighting falling on increasingly deaf ears.

"In the name of humanity, the violence must stop," pleaded UN Secretary General Ban Ki-moon after holding long talks with Israeli Prime Minister Benjamin Netanyahu, urging him to "stop the violence" and heed international calls for a ceasefire.

But Netanyahu appeared determined to press the offensive.

"We must be prepared for a lengthy campaign," he said in a live broadcast Monday after a mortar attack killed four people in southern Israel, and troops fought a gun battle with Palestinian militants who sneaked across the border.

"We will not end this operation without neutralising the tunnels whose sole purpose is killing our citizens."

As he spoke, the military sent messages to thousands of Palestinians in Shejaiya, Zeitun, Jabaliya, Beit Lahiya and Beit Hanun, urging them to flee their homes and seek shelter in central Gaza City as troops prepared to step up their 21-day campaign.

Shortly afterwards, the cloudy skies over Gaza lit up with flashes as the army began an intensive wave of air strikes and heavy shelling across the strip that continued early Tuesday, AFP correspondents and medics said.

Ten people were killed in the first wave of strikes, among them three children who died with two adults when a shell hit a house in the northern town of Jabaliya, emergency services spokesman Ashraf al-Qudra said.

Another five died in a strike on Khan Yunis in southern Gaza, taking to at least 29 the number of killed on Monday.

Early Tuesday, seven Palestinians died in an Israeli bombardment of the city of Rafah in the southern Gaza Strip and another six were killed in the Bureij refugee camp, taking to almost 1,100 the number of Palestinians who have died since the start of Israeli military operations.

The seven, including five women and one child, died when their three-storey building was destroyed, said the spokesman for Gaza rescue services.

Among the other six were three children and two women. Fifteen people were also wounded.

- Calm before the storm -

Monday had started with a deceptive air of calm in and around Gaza following a quiet second night in which both sides appeared to be observing an undeclared ceasefire.

Despite the lull, there was little mood for celebration in Gaza City as the three-day Eid holiday got under way, with families quickly leaving the mosque after prayers to head straight home or to pay their respects to the dead.

"This is the Eid of the martyrs," said Ahed Shamali mourning the death of his 16-year-old son.

But tensions rose sharply after medics said a shell had struck a building inside the Shifa hospital compound in Gaza City, which was quickly followed by reports of a blast hitting a children's playground in a beachside refugee camp, which left 10 dead, eight of them children.

The Israeli army categorically denied it had fired at either the hospital or the camp.

Residents in the Shati camp said an F-16 firing several missiles at a motorised rickshaw, with medics confirming 10 dead with another 46 injured, including many children.

Near the site of the blast, women wailed and men screamed in anguish in scenes of utter confusion and distress, an AFP correspondent said.

But the army denied any involvement, blaming errant rocket fire by Palestinian militants.

"We have not fired on the hospital or on Shati refugee camp," Major Arye Shalicar told AFP, saying the only drones used near Shifa were not equipped with missiles.

"We know that Hamas was firing from both areas and the missiles struck these places," he said, adding that 200 missiles fired at Israel had fallen short and landed inside Gaza in the past three weeks.

- Mortar shell kills four Israelis -

Shortly afterwards, a mortar shell struck southern Israel, killing four soldiers near a kibbutz opposite Gaza City, the army said. Another soldier died inside Gaza earlier Monday.

Media reports said another dozen people were wounded in the strike claimed by Hamas militants from the Ezzedine al-Qassam Brigades, which said it was revenge for the deaths in Shati camp.

Around the same time, troops in nearby area of southern Israel fought a gun battle with a group of militants who emerged from a cross-border tunnel close to a kibbutz, killing one of the gunmen, the army said.

That attack was also claimed by Hamas, which said its militants had carried out an "operation behind enemy lines", claiming they had killed a large number of soldiers.

As the violence soared, top diplomats from Britain, France, Germany, Italy and the United States pledged to step up the pressure to force the sides to accept a truce, with a statement from the French presidency saying they had "agreed to redouble their efforts to obtain a ceasefire.

"Pressure must increase to get there," it said.

US Secretary of State John Kerry said any lasting truce must ensure the disarmament of Hamas and other militant groups, with parties working together on the basis of an Egyptian ceasefire initiative.

And Palestinian president Mahmud Abbas was expected to visit Cairo with representatives of Hamas and Islamic Jihad for fresh talks with the Egyptians on ending the violence in Gaza, a senior source in Ramallah told AFP. (***)

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