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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 (local time), although the station retracted an earlier report that a truce had already been provisionally agreed.
Health officials said at least 84 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 Hamas and its militant allies.
Local hospital officials said this brought the total number of Palestinian dead in the conflict to 1,164, most of them civilians. On the Israeli side, 53 soldiers and three civilians have been killed.
The Israeli assault intensified after the deaths of 10 troops in Palestinian cross-border attacks on Monday, with Prime Minister Benjamin Netanyahu warning of a long conflict ahead.
But the military said it needed about a week to complete its main mission of destroying cross-border tunnels through which Hamas militants have infiltrated to attack Israelis.
Thick black smoke rose from blazing fuel tanks at the power station that supplies up to two-thirds of Gaza's energy needs. The local energy authority said initial damage assessments suggested 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 cubic 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. Gazans, who have had a few hours electricity a day since the conflict began, now face months without power.
Southern Gaza gets some power from neighbouring Egypt but electricity lines from Israel have been damaged during the war.
ROCKETS, TRUCE TALK
Palestinians launched 52 rockets toward southern and central Israel, including the Tel Aviv area, the military said, adding that five were shot down by Iron Dome interceptors while the rest fell wide, causing no damage or casualties.
Outside pressure has been building on Netanyahu to rein in his forces. 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.
An Egyptian official said Cairo was revising a truce proposal that Israel had originally accepted but Hamas rejected, and that the new offer would be presented to the Palestinian delegation expected 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," the Egyptian official told Reuters, an account that the Netanyahu government neither confirmed nor denied.
The West Bank-based Palestinian leadership, saying it was also speaking for Hamas and Islamic Jihad in the Gaza Strip, voiced support on Tuesday for a 24-72 hour ceasefire.
But Hamas spokesman Sami Abu Zuhri told Reuters the statement by senior Palestine Liberation Organization official Yasser Abed Rabbo did not reflect Hamas's position. "Hamas gave no approval to anything Abed Rabbo said," Abu Zuhri added.
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.
Local hospital officials said Israeli tank shells and air strikes killed 10 people in and around Jabalya refugee camp in the northern Gaza Strip, and that a doctor from the UNRWA relief agency and his brother were killed in another strike nearby.
MORE THAN 200,000 DISPLACED
UNRWA, the main U.N. agency in Gaza, said more than 200,000 displaced Palestinians had taken shelter in its schools and buildings, following calls by Israel for civilians to evacuate whole neighbourhoods before military operations. Thousands more have been taken in by friends or family.
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," said spokesman Chris Gunness.
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."
Israel launched its offensive saying it wanted to halt rocket attacks by Hamas and its allies. It later ordered a land invasion to find and destroy the warren of Hamas tunnels.
Hamas and Israel have set conditions for a ceasefire that appear irreconcilable.
Israel wants Gaza's armed groups stripped of weapons. Hamas and its allies want an Israeli-Egyptian blockade lifted.