* 28 members of one Gazan family killed in blast
* Israeli jets, tanks pound Gaza Strip day and night
* Palestinian death toll reaches 496, mostly civilians
* UN Security Council calls for immediate ceasefire
* US's Kerry due in Egypt to seek end to bloodshed
By Nidal al-Mughrabi and Crispian Balmer
GAZA/JERUSALEM, July 21 (Reuters) - Israeli forces killed 10 Palestinian militants who slipped across the border from Gaza through hidden tunnels on Monday, the military said, as the death toll from the two-week conflict passed 500 amid growing international calls for an end.
Defying a U.N. Security Council appeal for an immediate ceasefire, Israeli jets, tanks and artillery continued to pound the Gaza Strip, killing 28 members of a single family near the enclave's southern border with Egypt, medics said.
The Islamist group Hamas and its allies fired multiple missiles across southern and central Israel, and heavy fighting was reported in the north and east of Gaza.
Non-stop attacks lifted the Palestinian death toll to 496, including almost 100 children, since fighting started on July 8, Gaza health officials said. Israel says 18 of its soldiers have also died along with two civilians.
Despite worldwide calls for a cessation of the worst bout of Palestinian-Israeli violence for more than five years, Israeli ministers ruled out any swift truce.
"This is not the time to talk of a ceasefire," said Gilad Erdan, communications minister and a member of Israeli Prime Minister Benjamin Netanyahu's inner security cabinet.
"We must complete the mission, and the mission cannot end until the threat of the tunnels is removed," he told reporters.
For its part, Hamas, weakened by the loss of Egypt and Syria as allies, voiced determination to fight on to break Israel's economic siege of Gaza.
U.S. Secretary of State John Kerry was due to fly to Egypt later in the day as part of a gathering effort to halt the bloodshed, and U.N. Secretary General Ban Ki-moon is touring the Middle East trying to secure a ceasefire.
Past flare-ups between Israel and its foes in Gaza and Lebanon have usually ended when the United States, the Jewish state's guardian ally, calls a halt, sometimes hastened by a strike that inflicts high civilian casualties on the Arab side.
While Washington went along with Sunday's Security Council statement, it has so far defended Israeli actions and refrained from pressuring Netanyahu publicly to stop.
Violence along the Gaza border intensified on Monday and sirens wailed across much of central and southern Israel to warn of rocket attacks. At least nine missiles were shot down by Israel's Iron Dome interceptor, the army said.
Looking to take the fight onto Israeli soil, two groups of Palestinian fighters crossed from Gaza via two tunnels in the early morning, opening fire as they entered.
Black and white surveillance footage supplied by the army, showed one group of five or six men crouching and firing in long grass. Seconds later they were hit by a large explosion, which sent a cloud of smoke and debris flying into the air.
A military spokeswoman said at least 10 militants died. She did not comment on reports of casualties amongst Israeli forces. Hamas said its men had destroyed an army jeep in the assault.
Fighters from Hamas, which controls Gaza, and its allies, have repeatedly tried to infiltrate Israel over the past week through a vast network of hidden tunnels, looking to attack villages and army encampments that dot the border area.
Netanyahu sent in Israeli ground forces on Thursday to destroy the tunnels and the militants' missile stock pile.
Hamas announced late on Sunday its fighters had captured an Israeli soldier during fighting, setting off celebrations around Gaza. It named the man as Shaul Aron and showed his ID papers, but did not release any picture of him alive in their hands.
Israel's ambassador to the United Nations denied the claim, and the Israel's military said it was still investigating.
"We still cannot rule it out," military spokesman Lieutenant-Colonel Peter Lerner said on Monday.
A confident-sounding Hamas told Israel to quit Gaza.
"Israel has terribly failed and we advise them to take their soldiers and leave before we kidnap more soldiers in addition to the scores we have already killed and wounded," said the group's spokesman, Sami Abu Zuhri.
Any capture of an Israeli soldier would pile pressure on Netanyahu to intensify the military campaign.
He agreed to free more than 1,000 Palestinian prisoners in 2011 to secure the release of a soldier who was held for more than five years by Gaza, and officials have said they want to avoid any repeat of that prolonged drama.
Lerner told reporters that the main focus of fighting remained the Shejaia district, east of Gaza City, where some 72 Palestinians, many of them civilians, were killed on Sunday.
In its push against militants in Shejaia, Israel also suffered its worst losses in the offensive, with 13 soldiers killed - the army's heaviest one-day loss in battle since 2006.
The high death toll by Israeli standards appeared to cement a public mood of grim determination.
Many flags flew at half mast but no leading figures are calling into question the operation. "We need to continue to grit our teeth, to shut our ears, to ignore the background noise and to get the job done," columnist Ben Caspit wrote in Ma'ariv.
Israel's army said it had been targeting militants in the clashes, charging that they had fired rockets from Shejaia and built tunnels and command centres there. The army said it had warned civilians to leave two days earlier.
Sounds of explosions rocked Gaza City through the morning, with residents reporting heavy fighting in Shejaia and the adjacent Zeitoun neighbourhood. Locals also said there was heavy shelling in Beit Hanoun, in the northern Gaza Strip.
"It seems we are heading towards a massacre in Beit Hanoun. They drove us out of our houses with their fire. We carried our kids and ran away," said Abu Ahmed, he did not want to give his full name for fear of Israeli reprisals.
"It was a night of horror," the 50 year-old told Reuters.
At the other end of Gaza, medics said 28 members of the Abu Jamea family died when their house was hit by a bomb. Nearby, 10 members of the Seyam family died when they were hit by a tank shell as they tried to flee their house, officials said.
Kerry said on Sunday he supported Israel's efforts to destroy the Hamas tunnel network, but Washington has also said it is worried by the prospect of a further escalation.
Lerner said that since start of Israeli ground operations, the army had uncovered 43 access points to 16 different tunnels. (Additional reporting by Ari Rabinovitch in Jerusalem, Noah Browning in Gaza and Michelle Nichols at the United Nations; Writing by Crispian Balmer and Allyn Fisher-Ilan; Editing by John Stonestreet and Paul Taylor)