More than 100 Palestinians are said to have been killed as Israel intensified its bombardment of Gaza and a ceasefire proposal was rebuffed by Hamas.
Gaza's only power plant was hit as Israel carried out air strikes targeting sites linked to Hamas, the Islamist group which controls Gaza.
Israel intercepted rockets over central and southern parts of the country.
Later, Hamas turned down a ceasefire proposal from a senior Palestinian in the West Bank.
The proposal by Yasser Abed Rabbo of the Palestine Liberation Organization (PLO) came in the aftermath of a deadly series of air strikes overnight and on Tuesday morning.
He said a ceasefire was imminent and claimed to speak for Hamas, but a spokesman for the group quickly denied that.
As night fell an audio recording emerged attributed to Hamas' reclusive military leader, Mohammad Deif, asserting Hamas' position.
"We don't accept any condition of ceasefire," the Associated Press quoted the Hamas commander as saying. "There is no ceasefire without the stop of the aggression and the end of the siege."
Israel and Egypt have imposed a blockade on Gaza restricted the entry of goods since 2007.
Palestinian officials now say 1,156 Palestinians, most of them civilians, have been killed in the fighting since 8 July. Some 6,700 have been injured.
Israel has lost 53 soldiers and three civilians - two Israelis and a Thai worker.
Power plant destroyed
Gazans get power from just one local plant, as well as some supplies from Israel and Egypt.
On Tuesday morning a huge plume of smoke rose over the Strip's only power plant after one of its fuel tanks was reportedly set alight by Israeli tank shells, and the facility was forced to shut down.
At the scene: Martin Patience, BBC News, Gaza
For the last three weeks, most Gazans have been living with just a few hours of electrical supplies - now the situation will almost certainly get worse.
After a brief lull in the fighting earlier this week, the violence has returned with a renewed intensity.
In Gaza City you can hear the constant bombardment of areas close to the Israeli border. There have also been large explosions in the city throughout the morning.
Any sign that a patchwork of truces would lead to more a sustainable ceasefire has been dashed for now.
View from Israel: Bethany Bell, BBC News, Jerusalem
More than three weeks on, there is in general very widespread support among Israelis for the Gaza offensive. Recent polls say almost 90% of Israelis are in favour.
Some are beginning to ask whether the army and the government underestimated the tunnel threat from Gaza. Targeting the tunnels is one of Israel's main objectives in this campaign, but destroying them is complicated.
Israel says it has identified more than 30 tunnels - but the army was taken off guard last night when five soldiers were killed by Palestinian militants who came up through a tunnel into Israel.
Military sources say these aren't just single shafts but a labyrinth of underground passageways, some booby-trapped with explosives.
The government says it will not stop the offensive until the tunnels are destroyed.
Fifty-five houses were destroyed in overnight bombing, with people buried under rubble in at least three of them, Palestinian security sources told the BBC.
The unoccupied house of former Hamas Prime Minister Ismail Haniyeh was destroyed.
A neighbour, Um Hani Abu Ryalah, told AP news agency the experience had terrified her family: "Our children... can't hear because of the loud explosions and they are shaking."
Israeli fire is also said to have damaged the Hamas TV and radio stations, three mosques, four factories and government buildings.
Gaza's port had also been destroyed, Palestinian security sources told the BBC, and two schools and a kindergarten were on fire after being hit.
Among the 100 people killed on Tuesday were seven families, the Palestinian health ministry said.
UN Relief and Works Agency spokesman Chris Gunness said in a tweet that a number of staff members had reportedly been killed.
The UN is currently caring for 182,604 Palestinians in its 82 shelters in Gaza, he said.
Rockets fired from Gaza continued to hit Israel on Tuesday.
The Iron Dome anti-missile system intercepted four over the southern city of Beersheva, Israeli media reported. Sirens sounded in Tel Aviv and several other towns.
Lt-Col Peter Lerner, an Israeli military spokesman, told AP pressure was being increased on Hamas.
"Israel is determined to strike this organisation and relieve us of this threat," he said.
The renewed violence comes after Israel said 10 soldiers died on Monday: five were killed by an infiltrator near the border, four by a mortar strike, and another in fighting in southern Gaza.
In an address to Israelis on Monday night, Mr Netanyahu said Gaza had to be demilitarised in order to protect Israel.
"We will not finish the operation without neutralising the tunnels, which have the sole purpose of destroying our citizens, killing our children," he said.
Israel's Operation Protective Edge began on 8 July after a surge in militant rocket attacks.
A rally in support of the operation is planned for Tuesday evening in Tel Aviv.