* Shelling resumes in southern Gaza, 30 killed
* Ten dead in air attack on Gaza school
* Israel shuns Cairo truce talks while Palestinians go
* At least 1,777 Gazans killed; 67 dead on Israel's side
By Nidal al-Mughrabi and Ari Rabinovitch
GAZA/JERUSALEM, Aug 3 (Reuters) - An Israeli air strike killed 10 people and wounded about 30 on Sunday in a U.N.-run school in the southern Gaza Strip, a Palestinian official said, as dozens died in Israeli shelling of the enclave and Hamas fired rockets at Israel.
U.N. Secretary-General Ban Ki-moon described the attack as a "moral outrage and a criminal act" and called for those responsible for the "gross violation of international humanitarian law" to be held accountable.
The United States was "appalled by today's disgraceful shelling" and urged Israel to do more to prevent civilian casualties, according to a statement by State Department spokeswoman Jen Psaki. She also called for an investigation into recent attacks on U.N. schools.
It was the second strike on a school in less than a week.
The Israeli military said it had "targeted three Islamic Jihad terrorists on board a motorcycle in the vicinity of an UNRWA school in Rafah" and added it was "reviewing the consequences of this strike."
Islamic Jihad did not report any of its militants killed or injured in the incident. A Palestinian health official said all those wounded or killed were from inside the school.
Amid Hamas accusations that Israel had misled the world about the alleged capture of an Israeli soldier, the officer, Lieutenant Hadar Goldin, was buried on Sunday after the military said it recovered remains and he was killed in action.
Goldin's suspected abduction led to the collapse of a U.S.- and U.N.-brokered ceasefire on Friday. In Cairo, efforts to find a new truce were due to resume on Sunday.
With the fighting in its 27th day, Reuters TV footage showed a column of Israeli tanks and dozens of infantrymen leaving Gaza. But an Israeli military spokesman denied reports by Israeli and some U.S. media that most Israeli troops had been pulled out of the coastal enclave.
"We are redeploying and regrouping, and we have extensive forces both on the ground in Gaza and on the border at this time," Lieutenant-Colonel Peter Lerner said.
Israel's troops were "awaiting further orders and preparing a course of action for the next stage," Lerner said.
In the town of Rafah, where the military has been battling militants, a missile from an Israeli aircraft struck the entrance to the U.N.-run school, where Palestinians who had fled their homes were sheltering, witnesses and medics said.
Ashraf Al-Qidra, spokesman for the Gaza health ministry, said 10 people had been killed and 30 wounded, all from inside the school.
Robert Serry, U.N. Middle East Special Coordinator, said the school had been sheltering 3,000 displaced persons and the strike caused multiple deaths and injuries.
"It is simply intolerable that another school has come under fire while designated to provide shelter for civilians fleeing the hostilities," he said.
Last Wednesday, at least 15 Palestinians who sought refuge in a U.N.-run school in Jabalya refugee camp were killed during fighting, and the U.N. said Israeli artillery had apparently hit the building. The Israeli military said gunmen had fired mortar bombs from near the school and it shot back in response.
Earlier on Sunday, Israeli shelling killed at least 30 people in Gaza, a day after Prime Minister Benjamin Netanyahu vowed to keep up pressure on Hamas even after the army completes its core mission of destroying a tunnel network used by Palestinian militants to attack Israel.
Netanyahu says Gaza's dominant Hamas faction bears ultimate responsibility for civilian casualties, accusing gunmen and rocket-launching squads of using residents in densely populated areas as "human shields".
In Rafah, Fatah faction leader and local resident Ashraf Goma said locals were unable to deal with the casualties.
"Bodies of the wounded are bleeding in the streets and other corpses are laid on the road with no one able to recover them.
"I saw a man on a donkey cart bringing seven bodies into the hospital. Bodies are being kept in ice-cream refrigerators, in flower and vegetable coolers," Goma told Reuters.
The Israeli army said that more than 55 rockets had been fired from Gaza at Israel on Sunday. Shrapnel from a rocket shot down by Israel's Iron Dome interceptor fell inside a playground in the Tel Aviv area but caused no injury, media reports said.
Israeli troops had discovered a cache of 150 mortar bombs in the southern Gaza Strip. They had clashed with Palestinian fighters who emerged from a tunnel and with others preparing to launch an anti-tank missile from a house in the area, a military statement said.
Israel began its offensive against Gaza on July 8 following a surge of cross-border rocket salvoes by Hamas and other guerrillas.
The fighting on Sunday pushed the Gaza death toll given by Palestinian officials to 1,775, most of them civilians. Israel has confirmed that 64 soldiers have died in combat, while Palestinian rockets have also killed three civilians in Israel.
In new truce moves, a delegation from Hamas and the Islamic Jihad group arrived in the Egyptian capital, but a quick breakthrough seemed unlikely in the absence of Israeli representatives.
After accusing Hamas of breaching Friday's short-lived ceasefire, Israel said it would not send envoys as scheduled.
Israel says it wants Gaza demilitarised under any long-term arrangement.
Hamas, sworn to Israel's destruction, demands Israel withdraw its troops and a lifting of Israeli and Egyptian blockades that have choked Gaza's economy.
A Palestinian official said Palestinian representatives in Cairo had formulated a joint paper listing those conditions as well as demands for the release of Hamas prisoners held by Israel and the start of a Gaza reconstruction process.
In Gaza, Israel intensified attacks in the area of Rafah along the border with Egypt, where Goldin had been feared captured on Friday. Hamas described Israeli shelling in the town as unjustified retribution for what the group said was a false accusation that the officer had been abducted.
Defence Minister Moshe Yaalon said Goldin was a relative of his. "He and other soldiers who fell embarked on the campaign to restore quiet and security to Israel," he said.
The Israeli Ambassador to the United States, Ron Dermer, said three dozen tunnels had been unearthed and destroyed and "we are finishing up de-commissioning these tunnels".
"We hope that that job will be completed in a matter of hours, not days," he said on NBC's "Meet the Press".
(Additional reporting and Dan Williams in Jerusalem and Mostafa Hashem and Oliver Holmes in Cairo, Writing by Ori Lewis; Editing by Tom Heneghan)