About 70 people have been killed in the fighting on Thursday, Gaza's Ministry of Health said.
Reports said at least 15 rockets had been fired from Gaza into Israel since the early morning, injuring eight people in Beersheba.
Nearly 1,100 Gazans and 13 Israelis have reportedly died so far in the conflict.
Speaking to the press after meeting Israeli leaders in Tel Aviv, Mr Ban repeated previous calls for an immediate ceasefire, and said the suffering in Gaza was a "dire humanitarian crisis" that had reached an "unbearable point".
In other developments:
The UK Foreign Office minister Lord Malloch-Brown says the British government "utterly" condemns the attack on the UN headquarters in Gaza. Fierce criticism also came from the French foreign ministry
Two hospitals in Gaza City are hit by shellfire: the al-Quds hospital in Tel al-Hawa neighbourhood, scene of heavy fighting, and a Red Crescent hospital, the UK Red Cross says
The Shurouq tower block in Gaza City, which houses the offices of the Reuters news agency and several other media organisations, is hit by an explosion, injuring a journalist for the Abu Dhabi television channel
Leaders of the six-member Gulf Cooperation Council are to meet in Saudi Arabia to discuss the crisis. The Saudi monarch, King Abdullah, said the meeting was convened because of what he called Israeli aggression against the Palestinian people
A boat carrying medical supplies to Gaza is surrounded by Israeli warships in international waters off Lebanon's southern coast and forced to return to Cyprus, according to charity Free Gaza
Palestinian deaths in the Gaza Strip reach 1,083 according to Gaza medical sources. Nearly a third of the dead are said to be children
Israeli and Hamas envoys have been in Cairo, holding separate meetings with Egyptian negotiators.
Egypt has been leading efforts to broker a ceasefire that could include a peacekeeping force being deployed along its border with Gaza to prevent the smuggling of weapons.
On Wednesday, Hamas official Salah al-Bardawil said his movement had presented Egyptian negotiators with a "detailed vision" of how to bring about a ceasefire.
Hamas, which controls Gaza, has said any ceasefire agreement would have to include a halt to Israeli attacks, the complete withdrawal of Israeli forces and the opening of border crossings to end the blockade of Gaza.
Israeli government spokesman Mark Regev said there was "momentum" to the talks.
"Ultimately we want to see a long-term sustainable quiet in the south, a quiet that's going to be based on the total absence of all hostile fire from Gaza into Israel, and an internationally supported mechanism that will prevent Hamas from rearming," Mr Regev said.
Israel launched its offensive on the Gaza Strip on 27 December and has refused to allow international journalists to enter Gaza without supervision, making it to independently confirm casualty figures.
The offensive has provoked widespread international condemnation at the cost in civilian casualties and the ongoing humanitarian crisis in the coastal enclave.
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