* Hundreds of rockets hit Israel, jets strike Gaza
* Escalation follows weeks of tension in Jerusalem
* United Nations, U.S. focused on de-escalation (Adds gas platform shut down)
By Nidal al-Mughrabi and Jeffrey Heller
GAZA/JERUSALEM, May 12 (Reuters) - Israel said it killed 16 members of the Hamas military wing in a air strike on Gaza on Wednesday and Palestinian militants rained rockets into Israel as global concern mounted over their most intense hostilities in years.
At least 53 people have been killed in Gaza since violence escalated on Monday, according to the Palestinian territory's health ministry. Six people have been killed in Israel, medical officials said.
Israel's Shin Bet security service said the brigade commander for Gaza City was among senior members of the Islamist militant group Hamas who had been killed.
"This is just the beginning. We'll hit them like they've never dreamed possible," Prime Minister Benjamin Netanyahu said in a statement.
Soon after the announcement, a new rocket barrage was fired at the Israeli city of Ashdod and Israeli media said the military was preparing for new salvoes on the Tel Aviv area.
Hamas confirmed the commander's death and the loss of "other leaders and warriors" and said in a statement: "Thousands of leaders and soldiers will follow in their footsteps.".
A Palestinian source said truce efforts by Egypt, Qatar and the United Nations had made no progress to end violence that flared this week after tension during the Muslim fasting month of Ramadan and clashes in East Jerusalem.
The offensive is the heaviest between Israel and Hamas since a 2014 war in the Hamas-ruled enclave, and concern is growing that the situation could spiral out of control.
In Gaza, a multi-storey residential building collapsed after Israel warned its occupants in advance to evacuate, and another was heavily damaged in the air strikes.
Other air strikes hit what Israel's military said were rocket launch sites, Hamas offices and the homes of Hamas leaders. Israeli officials said at least 41 Palestinian fighters have been killed in the Gaza hostilities so far.
"Israel has gone crazy," said a man on a Gaza street, where people ran out of their homes as explosions rocked buildings.
Sixteen people were killed in Israeli air strikes on Gaza on Wednesday, Gaza's health ministry said. Witnesses and health officials in Gaza said one Israeli air strike killed three people, including a woman, in a car.
Many Israelis also spent a sleepless night as waves of rockets hit Israel's heartland.
"The children have escaped the coronavirus, and now a new trauma," an Israeli woman in the coastal city of Ashkelon told Channel 11 TV.
Israelis ran to shelters or lay flat on pavements in some communities far from Gaza.
"All of Israel is under attack. It's a very scary situation to be in," said Margo Aronovic, a 26-year-old student, in Tel Aviv.
Along the Gaza border, an Israeli soldier was killed by an anti-tank missile, the military said. Two people were killed by a rocket in Lod, near Tel Aviv.
Tension also spilled over in mixed Arab-Jewish towns in Israel where there have been demonstrations over the hostilities. A synagogue was torched in Lod.
Defence Minister Benny Gantz told reporters the Israeli military action would continue until "complete and long-term quiet" was achieved.
GAS PLATFORM SHUT DOWN
U.S. energy corporation Chevron said it had shut down the Tamar natural gas platform off the Israeli coast on the instructions of the Energy Ministry. Israel said its energy needs would continue to be met.
Hamas said it fired 210 rockets towards Beersheba in southern Israel and at Tel Aviv overnight in response to the strikes on the tower buildings in Gaza City.
"If they (Israeli forces) want to escalate, the resistance is ready, if they want to stop, the resistance is ready," Hamas leader Ismail Haniyeh said.
For Israel, the targeting of Tel Aviv, its commercial capital, posed a new challenge in the confrontation with Hamas, regarded as a terrorist organisation by Israel and the United States.
The violence followed weeks of tension during Ramadan, with clashes between Israeli police and Palestinian protesters near Al-Aqsa Mosque in East Jerusalem.
These escalated ahead of a court hearing - now postponed - that could lead to the eviction of Palestinian families from East Jerusalem homes claimed by Jewish settlers.
The conflict has led to the freezing of talks by Netanyahu's opponents on forming a governing coalition to unseat him after Israel's inconclusive March 23 election.
Violence has also flared in the occupied West Bank. Medical sources said a 16-year-old Palestinian was killed in clashes with Israeli forces on Wednesday. Gaza's health ministry said 14 of the people reported killed in the enclave were children. The Israeli military said it was looking into these reports and that preventing civilian casualties was a priority.
Israel has dispatched infantry and armour to reinforce tanks already gathered on the border, evoking memories of its last ground incursion into Gaza to stop rocket attacks in 2014.
Witnesses said Israeli aircraft destroyed Gaza's Hamas-run police headquarters in the city.
Although the latest problems in Jerusalem were the immediate trigger for hostilities, Palestinians have also been frustrated as their aspirations for an independent state have suffered setbacks in recent years.
These include Washington's recognition of disputed Jerusalem as Israel's capital, a U.S. plan to end the conflict that they saw as favourable to Israel, and continued settlement building.
(Reporting by Nidal al-Mughrabi, Dan Williams, Ari Rabinovitch and Rami Ayyub; Additional reporting by Stephanie Nebehay in Geneva, Nandita Bose and Steve Holland in Washington and Michelle Nichols in New York, and Stephen Farrell in Jerusalem; Writing by Kevin Liffey; Editing by Angus MacSwan and Timothy Heritage)
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