At least 100 Palestinians killed and media outlets, mosque and refugee camp all targeted as calls for ceasefire dismissed

Flames and clouds of black smoke billowed over Gaza's only power plant on after it was destroyed during the most relentless and widespread Israeli bombardment of the current conflict. At least 100 people were killed on Tuesday, according to Gaza health officials.

"The power plant is finished," said its director, Mohammed al-Sharif, signalling a new crisis for Gaza's 1.8 million people, who were already enduring power cuts of more than 20 hours a day.

Amnesty International said the crippling of the power station amounted to "collective punishment of Palestinians". The strike on the plant will worsen already severe problems with Gaza's water supply, sewage treatment and power supplies to medical facilities.

"We need at least one year to repair the power plant, the turbines, the fuel tanks and the control room," said Fathi Sheik Khalil of the Gaza energy authority. "Everything was burned." He said crew members who had been trapped by the fire for several hours were evacuated.

Gaza City officials said damage to the power station could paralyse pumps and urged residents to ration water.

Israeli fire killed another 21 Palestinians early on Wednesday, Gaza officials said. Tank shells pounding houses in eastern Jebalya in the northern Gaza Strip killed 13 people and wounded many others, health ministry spokesman Ashraf Al-Qidra said, with a medic and an infant among the dead.

Eight people, including five members of the same family in Jebalya, were killed in other strikes across the Gaza Strip.

Gaza hospital officials put the total number of Palestinians killed in the conflict at 1,224, most of them civilians. The UN said 182,000 people – around 10% of Gaza's population – had sought shelter in its premises.

On the Israeli side 53 soldiers and three civilians have been killed since the start of the offensive on 8 July.

The UN Relief and Works Agency (UNRWA) said it had found a cache of rockets at one of its schools in Gaza and deplored those who had put them there for placing civilians in harm's way. "This is yet another flagrant violation of the neutrality of our premises. We call on all the warring parties to respect the inviolability of UN property," said a spokesman. Israel has targeted some UNRWA sites in its current offensive and has in the past said the agency's property was being used for hostile purposes.

Israel intensified its military offensive after the prime minister, Binyamin Netanyahu, warned of a protracted campaign to achieve his goals in Gaza, launching strikes from air, land and sea.

Hopes of a new ceasefire in the three-week-old Gaza war rose momentarily on Tuesday afternoon when Yasser Abed Rabbo, a veteran Palestinian official, announced a 24-hour pause in fighting, saying he was speaking on behalf of Hamas and Islamic Jihad, the two main militant organisations.

But both parties to the conflict swiftly dismissed this.

Hamas's spokesman in Gaza, Sami Abu Zuhri, said the militant organisation in Gaza had not approved the announcement, and Israeli government spokesman Mark Regev said the proposal was "not serious". The rebuff from Hamas in Gaza indicated the gulf between it and the West Bank-based Palestinian leadership.

US secretary of state John Kerry said he was in discussions with Netanyahu to find an end to the fighting in Gaza. The pair had spoken "two, three, four times a day in recent days", Kerry told reporters in Washington.

They were working "very carefully and thoughtfully" on ways to "prevent this spiralling downwards", he added.

Kerry reiterated US support for Israel's right to self-defence, "to live free from rockets and tunnels". The secretary of state has come under sustained attack in Israel over what was perceived as undue sympathy for Hamas's position in ceasefire negotiations in the Middle East and Paris last week.

During a night and day of heavy pounding, Israeli forces targeted key symbolic and strategic targets, including the home of the Hamas leader in Gaza, Ismail Haniyeh, and an office building housing Hamas-controlled broadcast outlets.

In the most intense bombardment of the 22-day conflict, Gaza resident Mohamed al-Dalo said: "Missiles were falling like rain." He told the AFP news agency: "We all left our homes, some running in one direction, some in another; nobody knew which way to go."

Haniyeh's home was hit by a missile shortly before dawn, causing damage but no injuries. Most of Hamas's senior leaders are presumed to be residing in underground bunkers for the duration of the war.

"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."

Al-Aqsa TV and radio were also targeted. The TV station kept broadcasting, but the radio station went off air. The Israeli military said the stations were used to "transmit orders and messages to Hamas operatives and to instruct Gaza residents to ignore IDF warnings regarding upcoming military activity in specific areas".

Eleven people were killed in a strike on a house in Bureij refugee camp in Gaza City. A central mosque and government buildings were also targeted.

As sirens warning of rocket fire sounded across southern Israel for much of the day, the IDF said it had killed five militants emerging from a tunnel in the south of Gaza. It also disclosed that five Israeli soldiers had died in a gun battle on Monday with militants who crossed into Israel via a tunnel near the community of Nahal Oz, close to the border with the Gaza Strip.

David Cameron, the British prime minister, added his weight to growing international calls for an "unconditional, immediate humanitarian ceasefire".

"What we're seeing is absolutely heartbreaking in terms of the loss of life, and the pictures that everyone has seen on their television screen are really heart-rending and everyone wants to see this stopped, so an immediate unconditional ceasefire, that is what is required," he said. Blaming Hamas for triggering the current conflict, he added: "Hamas must stop attacking Israel with rocket attacks. That is how this started. It's completely unjustified and they need to stop as part of the ceasefire."

The IDF continued to categorically deny that its forces were responsible for hits on Shati refugee camp and the Shifa hospital on Monday. Eight children and two adults were killed at Shati while playing in a park.

The military released an aerial photograph it said showed rockets fired by militants had fallen short. In a statement it said that red lines drawn over the photograph indicated "the paths of the four terrorist rockets, as detected by IDF radars and sensors, that were launched in the attacks that resulted in one hitting the al-Shifa hospital and one hitting the Shati refugee camp. Of the other two rockets, one landed at sea, and the other was intercepted on its way to the city of Ashkelon."

Witnesses in Gaza said missiles had been fired from Israeli F-16s. A spokesman for the interior ministry in Gaza, Iyad al-Buzm, said explosives experts from Gaza police had examined "the targeted places and the remnants of shells there" as well as the wounds on the bodies, determining them to be inflicted by an Israeli strike.