* Diplomatic pressure building, delegates head to Cairo
* Electricity cut as Gaza's only power station knocked out,
* Hamas airs video of cross-border tunnel raid on army
* More than 1,200 Palestinians killed, 56 on Israeli side (Adds UN comment, Hamas video, Israeli poll, updates death toll)
By Nidal al-Mughrabi and Dan Williams
GAZA/JERUSALEM, July 29 (Reuters) - Israel knocked out Gaza's only power plant and pounded dozens of other high-profile targets on Tuesday, while Egyptian mediators prepared a revised proposal for halting its war with Islamist guerrillas in the enclave.
Israel's Channel Two TV said progress was being made on such a deal in Cairo, where a Palestinian delegation is expected later on Tuesday, although the station retracted an earlier report that a truce had already been provisionally agreed.
Health officials said at least 85 Palestinians died in some of heaviest bombardments from air, sea and land since Israel's offensive began on July 8 in response to rocket salvoes fired by Gaza's dominant Hamas Islamists and their guerrilla allies.
Local hospital officials put the total number of Palestinian dead in the conflict at 1,200, most of them civilians. On the Israeli side, 53 soldiers and three civilians have been killed.
UNRWA, the main U.N. relief agency in Gaza, said it was at "breaking point" with more than 200,000 Palestinians having taken shelter in its schools and buildings following calls by Israel for civilians to evacuate whole neighbourhoods before military operations.
The Israeli assault intensified after the deaths of 10 soldiers in Palestinian cross-border attacks on Monday, with Prime Minister Benjamin Netanyahu warning of a long conflict ahead.
The army said it needed about a week to complete its main mission of destroying cross-border infiltration tunnels and there has been strong Israeli public support for holding course.
In a bid to boost Palestinian morale and demoralise Israel, Hamas TV aired footage it said showed its fighters using a tunnel to reach an army watchtower on Monday. They are seen surprising an Israeli sentry, at which point they open fire and storm the watchtower compound to surround a fallen soldier.
Mohammed Deif, the shadowy leader of Hamas's armed wing, said in a voiceover message in the broadcast that Palestinians would continue confronting Israel until its blockade on Gaza - which is supported by neighbouring Egypt - was lifted.
"The occupying entity will not enjoy security unless our people live in freedom and dignity," Deif said. "There will be no ceasefire before the (Israeli) aggression is stopped and the blockade is lifted. We will not accept interim solutions."
ISRAEL DEMANDS DISARMAMENT
Israel has balked at freeing up Gaza's borders under any de-escalation deal unless Hamas's disarmament is also guaranteed.
Egypt said it was revising an unconditional truce proposal that Israel had originally accepted but Hamas rejected, and that the new offer would be presented to a Palestinian delegation expected in Cairo later on Tuesday. An Israeli official said Israel might send its own envoy to Cairo in the evening too.
"We are hearing that Israel has approved a ceasefire but Hamas has not," an Egyptian official told Reuters, an account that the Netanyahu government neither confirmed nor denied.
The U.S.-backed administration of Palestinian President Mahmoud Abbas in the Israeli-occupied West Bank, saying it was also speaking for Hamas and Islamic Jihad in the Gaza Strip, voiced support on Tuesday for a 24-72 hour ceasefire.
Hamas spokesman Sami Abu Zuhri disputed that statement but confirmed there were "intensive, ongoing contacts" on a truce.
Outside pressure has been building on Netanyahu to rein in his forces, while few Israelis want the operation to end now.
A Tel Aviv University poll published on Tuesday found 95 percent of Israel's Jewish majority felt the offensive was justified. Only 4 percent believed too much force had been used.
Both U.S. President Barack Obama and the U.N. Security Council have called for an immediate ceasefire to allow relief to reach Gaza's 1.8 million Palestinians, followed by negotiations on a more durable end to hostilities.
Efforts led by U.S. Secretary of State John Kerry last week failed to achieve a breakthrough, and the explosion of violence appeared to dash international hopes of turning a brief lull for the Muslim Eid al-Fitr festival into a longer-term ceasefire.
Hamas preaches the Jewish state's destruction but has in the past been open to long-term ceasefires. As it is shunned by the United States and Israel as a terrorist group, Kerry's mediation has been facilitated by Egypt, Turkey, Qatar and Abbas.
Thick black smoke rose from blazing fuel tanks at the power station that supplies up to two-thirds of Gaza's energy needs. Officials said the plant could be out of action for a year.
Electricity was cut to the city of Gaza and many other parts of the Hamas-dominated territory after what officials said was Israeli tank shelling of the tanks containing about 3 million litres of diesel fuel.
"The power plant is finished," said its director, Mohammed al-Sharif. An Israeli military spokeswoman had no immediate comment and said she was checking the report.
Gaza City municipality said damage to the station could halt many of the area's water pumps, and it urged residents to ration water consumption. South Gaza gets some power from neighbouring Egypt. Power lines from Israel have been damaged during the war.
Palestinians launched 54 rockets towards southern and central Israel, including the Tel Aviv and Jerusalem area, the military said, adding that five were shot down by Iron Dome interceptors while the rest fell wide, causing no damage.
The Israeli military said soldiers killed five gunmen who opened fire after emerging from a tunnel inside the Gaza Strip and that 110 targets were struck in the enclave on Tuesday. They included four weapons caches, which the military said were hidden in mosques, and a rocket launcher near another mosque. Residents said 20 houses were destroyed and two mosques hit.
Hospitals said tank shells and air strikes killed 12 people in north Gaza, including an UNRWA doctor and his brother.
UNRWA said it found a rocket cache in one of its central Gaza schools on Tuesday, the third such incident.
"This is yet another flagrant violation of the neutrality of our premises. We call on all the warring parties to respect the inviolability of U.N. property," spokesman Chris Gunness said.
He added that UNRWA would find it impossible to cope with a further influx of refugees to its shelters, warning that tens of thousands of people would soon be stranded on Gaza's streets.
"We have reached breaking point with this massive wave of human displacement. This will leave the warring parties, especially the government of Israel, to assume direct responsibility" for the displaced Palestinians, Gunness said.
Before dawn, Israeli aircraft fired a missile at the house of Hamas deputy leader Ismail Haniyeh, a former Palestinian prime minister, destroying the structure but causing no casualties, Gaza's Interior Ministry said.
"My house is not dearer than any of the houses of our people," Haniyeh was quoted as saying on a Hamas website. "The destruction of stones will not break our will and we will continue our resistance until we gain freedom."
Hamas, whose internal political leadership is in hiding, said its broadcasters Al-Aqsa TV and Al-Aqsa Radio were also targeted. The television station continued to broadcast but the radio station went silent.
The military said the stations were used to "transit orders and messages to Hamas operatives and to instruct Gaza residents to ignore IDF (Israel Defence Forces) warnings regarding upcoming military activity in specific areas." (Additional reporting by Michelle Nichols in New York and Yasmine Saleh in Cairo, Writing by Maayan Lubell and Dan Williams; Editing by Jeffrey Heller, Paul Taylor, David Stamp and Giles Elgood)
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