Secretary of State John F. Kerry met with Israeli Prime Minister Benjamin Netanyahu on Thursday to urge him to tone down his rhetoric and said he was “cautiously encouraged” that a wave of violence in Israel could be quelled.

After talking with Netanyahu for four hours, Kerry said he had some ideas he intends to discuss with Palestinian President Mahmoud Abbas and Jordan’s King Abdullah when they meet Saturday in Amman, Jordan. He provided no details, however, of his talks with Netanyahu.

“I would characterize that conversation as one that gave me a cautious measure of optimism that there may be . . . a way to defuse the situation and begin to find a way forward,” Kerry told reporters at a news conference with German Foreign Minister Frank-Walter Steinmeier. “If parties want to try, and I believe they do, want to move to a de-escalation, there are a set of choices that are available.”

The United States has grown increasingly alarmed over a lethal round of violence that has erupted in Israel this month. Nine Israelis have been killed, mostly in stabbing attacks by Palestinian youths. About 50 Palestinians have been killed, almost half of them identified by Israel as attackers.

The tensions are centered on the al-Aqsa Mosque compound in the Old City of Jerusalem, which is the third-holiest site in Islam and is revered by Jews as the site of two ancient temples. Under a decades-old agreement, Israel has maintained the status quo, an arrangement that allows Jews to visit the site but not to pray there. Rumors have spread among Palestinians that Israel wants to upend the unwritten understanding and grant Jews more access, though Netanyahu has labeled the rumors “lies.”

Israelis and Palestinians have been killed as violence spikes in recent weeks in the region. There is no one reason for the chaos, but the surge in Palestinian attacks comes down to politics, personal grievances and religion. (Jason Aldag/The Washington Post)

Kerry is seeking to persuade Israeli and Palestinian leaders to tamp down the accusatory rhetoric, believing it has helped fuel the wave of violence.

In his public statements, Netanyahu struck a combative tone, accusing the Palestinians again of lying about Israel and fomenting almost all the violence.

“There is no question that this wave of attacks was driven directly by the incitement, the incitement of Hamas, the incitement of the Islamist movement in Israel and the incitement, I am sorry to say, from President Abbas and the Palestinian Authority,” Netanyahu told reporters before meeting with Kerry.

The Israeli newspaper Haaretz reported that Netanyahu insisted to Kerry that the Palestinian Authority and Jordan, which is custodian of the al-Aqsa Mosque compound, must state clearly that the status quo has not been violated.

State Department spokesman John Kirby characterized the talks as “constructive.”

“A number of constructive proposals were suggested, including steps Israel could take to reaffirm yet again the continued commitment to maintaining the status quo at Temple Mount/Haram al-Sharif,” Kirby said. “Both agreed on the need to stop incitement, reduce tension and restore calm.”

Before meeting with Germany’s Steinmeier, Netanyahu told reporters that only Israel can be trusted to protect and ensure access to the holy sites.

“When you look around at the Middle East with the militant Shiites and militant Sunnis blowing up each other’s mosques and world heritage sites, let alone churches and synagogues, we’re the only ones that guarantee the integrity of the holy sites and the freedom of worship and access to all,” the Israeli leader said.

The almost daily stream of attacks in the region has alarmed diplomats who fear the violence may soon spiral out of control. U.N. Secretary-General Ban Ki-moon made a surprise visit to Israel and the West Bank this week pleading for calm. He later delivered a pessimistic assessment of the situation to the U.N. Security Council.

Even as Kerry and Netanyahu were talking, the violence continued.

In the city of Beit Shemesh, about 15 miles west of Jerusalem, a Palestinian attacker was fatally shot by police Thursday after stabbing an Israeli man, authorities said. In Jerusalem, an Israeli soldier shot and killed a Jewish man suspected of being an attacker. The man scuffled with police late Wednesday after he was asked to show identification, said Israeli police spokesman Micky Rosenfeld.

Kerry alluded to the fear that an even broader conflict is on the horizon, saying that if calm can be restored, attention must then turn to finding a permanent resolution. “If anything, what’s happening now is an urgent call to all with any responsibility . . . to help try to resolve age-old differences in a frozen conflict,” he said.

Diplomats from the United States, the European Union, Russia and United Nations — all involved as Middle East mediators and known as the Quartet — will meet in Vienna on Friday to discuss ways to ease the tension. Federica Mogherini, the E.U. foreign policy chief, echoed Kerry’s road map, saying the meeting’s priority is to encourage both sides to avoid making inflammatory speeches.

The Israeli prime minister is facing a barrage of criticism for comments he made Tuesday that the mufti of Jerusalem gave Hitler the idea of killing Jews during World War II. In a speech to the World Zionist Congress, Netanyahu tried to link the historic incitement against European Jews to the current Palestinian allegations that Israel is a threat to the al-Aqsa Mosque.

Ruth Eglash in Jerusalem contributed to this report.