Kim Hjelmgaard

USA TODAY

Israel's military canceled most travel permits for Palestinians during the Muslim holy month of Ramadan and deployed more troops to the West Bank Thursday after gunmen identified by police as Palestinian cousins from Hebron killed four Israelis at a popular food market in Tel Aviv.

The attack Wednesday on the Sarona Market, located across the street from the Israeli military’s headquarters, was among the deadliest and most brazen attacks in a nine-month wave of violence.

One Israeli witness, who was sitting at an upscale restaurant, told The Jerusalem Post the attackers looked like "wealthy Italian businessmen in fancy suits and skinny ties.” She said the pair had a “cold, calm look on their faces as they fired everywhere.”

Prime Minister Benjamin Netanyahu said a third person was arrested Thursday as an accomplice to the attack, the newspaper Haaretz reports.

In response, Israel froze 83,000 permits for Palestinians in the West Bank and Gaza to visit family in Israel, attend Ramadan prayers in Jerusalem or travel abroad via Israel’s Tel Aviv airport, COGAT, an Israeli defense body, said Thursday. The military also suspended Israeli work permits for 204 of the attackers’ relatives.

Police identified the victims as Michael Feige, 58, a sociologist and anthropologist at Ben-Gurion University, and Ido Ben Arieh, 42, a veteran of an elite army unit and executive at the Coca-Cola Co.’s Israel branch. Two other victims were identified as Ilana Naveh, 39, and Mila Misheiv, 32.

In a statement Thursday, colleagues at the university’s Institute for the Study of Israel and Zionism said they were “stunned by the incomprehensible loss of Feige.”

“Michael was a friend, scholar and teacher,” the statement said, according to the Associated Press. “Above all, Michael was the incarnation of a man of reason, tolerance and peace.”

As Israel convened a meeting of the diplomatic-security cabinet, new defense minister Avigdor Lieberman said he had "no intention of settling for lip service" in response to the attack, according to the newspaper Haaretz. Lieberman is leader of an ultranationalist party known for his hard-line views toward Palestinians.

Israel's military said two additional battalions made up of soldiers from infantry and special forces would go to the West Bank as part of new security measures.

Israeli police: 4 dead in terrorist attack at Tel Aviv market

COGAT said Palestinians would be prevented from leaving and entering the West Bank village of Yatta, home to the attackers, with exceptions made for humanitarian or medical cases.

"A village that has terrorists leaving from its midst will pay the price," said deputy defense minister Eli Ben-Dahan, Haaretz reported.

Ahmad Mussa Mahmara, the father of one of the attackers, said his son has two uncles serving life sentences in Israeli prison.

“We didn’t expect this. My son is young and has been in Jordan for the past four years, and just came here for the past five months. He does not have any political affiliation,” Mahmara said.

The military interrogated Mahmara on Wednesday night at his home, where his son was staying. Soldiers took measurements of the home in preparation for demolishing it, the military said, according to AP.

Israelis have been targeted by Palestinians in a wave of stabbings and shootings since the fall. At least 31 Israelis have died in the attacks and more than 200 Palestinians — the majority of them attackers, according to Israel — have been killed.

Prime Minister Benjamin Netanyahu called the latest attack a “cold-blooded murder by despicable terrorists.”

Hamas, the militant group that rules Gaza, welcomed the attack and called it a "heroic operation," but did not claim responsibility for it.