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TEL AVIV, Israel — Two Israeli battalions were sent to the West Bank on Thursday after two Palestinians fatally shot four people at a Tel Aviv mall.

The buildup would include hundreds of troops in "accordance with situation assessments," according to the Israel Defense Forces statement. They would not give any more details on the numbers involved.

Israel also revoked 83,000 permits for Palestinians living in Gaza and the occupied West Bank to travel abroad and attend Ramadan prayers in Jerusalem. In the past, restrictions on access to the Al-Aqsa Mosque compound, the holy site in the heart of Jerusalem's Old City that Jews call Temple Mount, have increased tensions.

Wednesday night's shooting was one of the deadliest attacks in an eight-month wave of violence. It occurred at Sarona Market, a popular tourist spot filled with shops and restaurants located across from Israel's military headquarters. The area, which is also popular with soldiers in uniform, sent families running for their lives.

Police identified the those killed as Ilana Nave, 39; Mila Mishayev, 32; Ido Ben Aryeh, 42; and Michael Feige, 58.

Two suspects — described by police as cousins aged in their 20s from the Hebron area — were captured. One was wounded.

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Israel also froze work permits for 204 of the alleged attackers' relatives and barred Palestinians from leaving and entering Yatta where the two are from, according to The Associated Press.

Newly appointed Defense Minister Avigdor Lieberman visited Sarona and expressed his condolences to the families of the victims on Thursday.

"I'm not going to speak and elaborate on are the steps we intend to take, but I'm sure I'm not going to settle for just talking," he told journalists.

On Wednesday night, Israeli Prime Minister Benjamin Netanyahu toured the same area and described that act as "cold-blooded murder."

The State Department condemned the shooting, saying in a statement: "These cowardly attacks against innocent civilians can never be justified."

Mahmoud Abbas, the president of the Palestinian Authority, reacted to the attack by condemning "all operations against civilians from any side, no matter the justification."

"The achievement of a just peace, and creating positive environments, is what contributes to remove and reduce the causes of tension and violence in the region," he said in a statement published by Palestinian news agency Wafa.

Israeli officials have denounced Abbas for not being sufficiently critical of such attacks, and accused him and other Palestinian leaders of inciting violence.

The father of one of the suspects told NBC News his son Khalid, a 21-year-old engineering student at the University of Jordan, had left the house saying he was going to get a laptop fixed.

When hadn't returned late into the evening Mohammed Mussa Makhamreh called his son's cellphone but got no answer.

"I was shocked to hear in the media and the internet and to see the name of my son, see that he is one of the attackers," the 49-year-old lawyer said.

Makhamreh said that while his son never mentioned anything about the political situation, Israel's occupation of the West Bank and the population's "daily suffering" could well be one of the factors behind the attack.

The father of the second suspect told Reuters he was also surprised at hearing the news.

Members of an Israeli ZAKA (Identification, Extraction and Rescue) team work at the scene of the shooting outside a restaurant in Sarona Market on Wednesday night in Tel Aviv, Israel. Getty Images

"I didn't expect this of him, I don't know what pushed him to do this, who organized this with him — I have no idea," said Ahmad Makhamreh. "The boy is a worker, he does not have any political leanings."

Meanwhile, Hamas, the Islamist militant group that rules Gaza, welcomed the shooting but did not claim responsibility for it.

Hamas official Mushir al-Masri called it a "heroic operation" and the group later issued an official statement promising the "Zionists" more "surprises" during the Muslim holy month of Ramadan.

Since October last year, 32 Israelis and two visiting U.S. citizens have been killed by Palestinians. Israeli forces have shot dead at least 196 Palestinians, 134 of whom Israel has said were assailants. Others were killed in clashes and protests.