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Texas Sen. Ted Cruz called U.S. Secretary of State John Kerry "utterly unfit" for his job and wants the country's chief diplomat to resign from his post if he does not disavow remarks he made recently saying that Israelis bear some of the responsibility for the recent string of violence in their country.

"It is utterly unacceptable that a senior official in the U.S. government would make such an unfounded slur against Israel, which has been our invaluable ally in the fight against terrorism," Cruz said in a statement sent to the press.

"Once again, Sec. Kerry and his staff have proven themselves utterly unfit for the positions they hold," he added.

Cruz, who has been a staunch opponent of the Obama administration's policies toward Israel, made his statement after hearing State Department spokesman John Kirby during a press briefing this week.

"I would say certainly individuals on both sides of this divide are – have proven capable of and in our view guilty of acts of terror," Kirby said in response to a question.

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Cruz's statement Thursday night came at a time of heightened tensions between Israel and the Palestinians.

On Friday morning, dozens of Palestinians threw firebombs at a West Bank site revered by some Jews as the tomb of biblical patriarch Joseph, a popular prayer site in recent years among some religious Jews.

Footage on local media shows flames leaping from the small stone structure in the West Bank city of Nablus. Palestinian security forces eventually extinguished the blaze.

Over the past month, eight Israelis were killed in Palestinian attacks, most of them stabbings. In that time, 31 Palestinians were killed by Israeli fire, including 14 labeled by Israel as attackers, and the rest in clashes with Israeli troops.

The violence has unnerved a jittery Israel, and prompted the U.S. on Saturday to issue a fresh call for restraint by all sides.

On Saturday, a 16-year-old Arab attacked two Israelis who were walking from the Old City toward the city center, said police spokesman Micky Rosenfeld. Police opened fire, killing the attacker. The two victims were lightly wounded, Rosenfeld said.

Later, just outside the Old City, another Palestinian stabbed two police officers, one in the neck. Rosenfeld said other police forces opened fire and killed the attacker, but also wounded one of their own. Three officers were taken to a hospital, one in serious condition.

The violence, including an apparent revenge attack in which an Israeli stabbed and wounded four Arabs on Friday, as well as increasing protests by Israel's own Arab minority, has raised fears of a new Palestinian intifada, or uprising.

Kerry on Thursday condemned the recent spate of terrorist attacks on Israeli civilians, saying there was no justification for violence and offering a more full-throated support for the Jewish state than previous U.S. statements.

Kerry, who plans to visit the Mideast next week, said the United States backs Israel's "right to defend its existence."

In a speech at Indiana University, he told a crowd that included former Republican and Democratic members of Congress that he was working with the Israelis and the Palestinians "to stabilize the situation."

"We strongly condemn the terrorist attacks against innocent civilians," Kerry said. "There is absolutely no justification for these reprehensible attacks."

Kerry's condemnation of the recent attacks on Israelis, however, seems to have done little dissuade Cruz from condemning the Obama administration's policies in the region.

"The Obama Administration is the most hostile we have seen towards the nation of Israel in our nation's history. In the last few days, this obsessive antagonism has been on full display," Crzu said. "We must immediately and unconditionally reject the delusion that the coordinated Palestinian frenzy of bloodlust is in any way legitimate. There is no moral equivalence here between the savagery of the Palestinian terrorists and the innocent Israelis they are trying to murder."

Cruz, who is running for the Republican presidential nod, previously called for Kerry's resignation in April 2014, when the secretary of state said Israel could become an "apartheid state" if it did not work out concessions with the Palestinians, and he was one of three senators to vote against Kerry's confirmation in 2013.

The Associated Press contributed to this report.

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