With 18 soldiers killed in Gaza, the highest military casualty toll in eight years, Israel is in mourning, but has vowed to pursue its mission against Hamas militants.

Thirteen of them were killed on Sunday alone, making it the bloodiest single day for the army since the 2006 war in Lebanon, with the press branding it "a "dark day".

The Israeli death toll has shot up since late Thursday when the Jewish state began the ground phase of a two-week operation to stamp out militant rocket fire and destroy Hamas tunnels in the besieged Palestinian territory.

Monday's newspapers were splashed with obituaries of the victims - all of whom belonged to the elite Golani Brigade - with President Shimon Peres expected to visit all of their families.

"My son was an extraordinary human being. He carried the mantle of his father, who was also in Golani," one grieving mother told public radio.

"13 heroic brothers" was the headline in the Israel HaYom freesheet, reflecting the nationwide sense that the fallen were all "family".

All Jewish Israelis must do military service, with men serving three years and women two.

Sunday's bloodshed raised to 20 the overall number of Israelis killed, two of whom were civilians hit by rocket fire.

Writing in the top-selling Yediot Aharonot, Sima Kadmon said the losses would hit the Israeli leadership hard.

"These are precisely the things that (Prime Minister Benjamin) Netanyahu and (Defence Minister Moshe) Yaalon sought to avoid," she wrote.

But so far, despite a painful reminder of the cost of a military ground operation against Hamas in Gaza, there has been no noticeable drop in support for the campaign.

And the toll has been far, far higher on the Palestinian side, where more than 500 have been killed since Operation Protective Edge began on July 8, most of them civilians, a spokesman for Gaza's emergency services said.

- 'All options on table' -

Despite Sunday's blow, Netanyahu has vowed to push ahead.

"We have to be strong in difficult days like today, and even in days which may yet come," he said after the casualties were announced. "We are in a war over our home."

He said there was "very strong" world support for the offensive, the worst confrontation in more than five years.

"We are carrying out a complex, deep, intensive activity inside the Gaza Strip and there is world support for this ... very strong support within the international community for the activity that the IDF is doing," he said.

Netanyahu said Israel had won "international legitimacy" for its military operation after accepting an Egyptian truce proposal that was shunned by Hamas.

But as world efforts to broker a new ceasefire gathered steam, there seemed to be little appetite for a halt to the hostilities, with Intelligence Minister Yuval Steinitz refusing to rule out a further escalation.

"All options are on the table," he told public radio.

"I think fighting risks continuing for a long time. We might have no other choice than to expand operations, including (possibly) taking full control of the Gaza Strip," he said while visiting the war wounded.

And Communications Minister Gilad Erdan said it was "not the moment for talk of a ceasefire", ruling out any withdrawal before ensuring there were "long-term arrangements in place" that would ensure a demilitarisation of the enclave.

Writing in the left-leaning Haaretz newspaper, defence correspondent Amos Harel said the soldiers' deaths would put increasing pressure on Netanyahu who would have to chose carefully which way he would go.

"The pressure on him and the government is mounting. There is enormous sensitivity in Israel to losing soldiers in combat. Paradoxically, it is greater than the sensitivity to the loss of civilian lives," he wrote.

"One should not envy Prime Minister Netanyahu and his cabinet who must now decide whether to expand the ground operation or whether to stick to the original plan of locating attack tunnels and destroying Hamas infrastructure, with the aim of quickly reaching a ceasefire."

US condemns attack on Egyptian soldiers
Washington (AFP) July 21, 2014 - The United States on Monday condemned a weekend attack on an Egyptian border checkpoint which left 21 soldiers dead, and vowed to keep up support for Egypt's security.

"We extend our condolences to the families of the victims, and hope for the quick and full recovery of the wounded," deputy State Department spokeswoman Marie Harf said in a statement on the attack, which took place near Egypt's desert frontier with restive Libya.

"A prosperous and dynamic Egypt requires an environment of security and stability, and the United States continues to support the Egyptian government's efforts to counter the threat of terrorism in Egypt as part of our commitment to the strategic partnership between our two countries."

The Egyptian military said militants firing machineguns and rocket-propelled grenades attacked a border checkpoint on Saturday, killing 21 soldiers in one of the biggest assaults on security forces in years.

The attack in a desert area 630 kilometres (390 miles) west of Cairo also left four soldiers wounded, the military said in a statement, blaming "terrorists."

Militants have stepped up attacks on the security forces since Islamist president Mohamed Morsi was toppled in July 2013 as the army struggles to quell an Islamist insurgency that has killed scores of soldiers and police, mainly in the Sinai Peninsula bordering Israel and the Palestinian Gaza Strip.

Harf's statement came just after US Secretary of State John Kerry arrived in Cairo on a delicate mission to broker a truce between Israel and the Palestinian Islamic movement Hamas in the Gaza Strip.