Updated

U.S. Secretary of State John Kerry expressed a "cautious measure of optimism" on Thursday following a meeting with Israeli Prime Minister Benjamin Netanyahu on solutions to quell the deadly month-long wave of violence in Israel.

Kerry told reporters that he planned to discuss the peace proposals with Palestinian President Mahmoud Abbas and Jordan's King Abdullah in a meeting Saturday in Jordan's capital.

"I come directly from several hours of conversation with Prime Minister Netanyahu and I would characterize that conversation as one that gave me a cautious measure of optimism that there may be some things that may be in the next couple of days put on the table which would have an impact -- I hope," Kerry said.

The meeting comes hours after an Israeli soldier shot and killed a Jewish man he suspected was a Palestinian "terrorist" in Jerusalem, police said, in a reflection of the jittery mood that has gripped Israelis amid a spate of near-daily Palestinian stabbing attacks.

Police spokesman Micky Rosenfeld said the man refused to show his I.D., scuffled with Israeli soldiers and then attempted to seize one of their weapons. One soldier shot the man, who later died of his wounds, Rosenfeld said.

Netanyahu has blamed President Abbas for inciting the violence and encouraging young Palestinians to kill. But Palestinians say the violence is rooted in frustration at decades of living under Israeli occupation.

"I think it is time for the international community to say clearly to President Abbas to stop spreading lies about Israel," Netanyahu told Kerry Thursday. "Lies that Israel wants to change the status quo at the Temple Mount, lies that Israel wants to tear down the Al-Aqsa Mosque, lies that Israel is executing Palestinians. All of that is false."

The recent tensions were first sparked over rumors that Israel was plotting to take over the sensitive Jerusalem holy site revered by both Jews and Muslims. The violence was initially confined to traditionally Arab east Jerusalem but soon spread deep into Israel, the West Bank and the Gaza Strip.

Earlier this week, an Israeli security guard shot an Eritrean migrant he thought was a Palestinian attacker. Police said the autopsy showed the man died from gunshot wounds and that four suspects would appear in court Thursday over the beating.

Israelis have scrambled to purchase pepper spray for self-defense and some government officials have called for citizens to carry firearms for protection.

Israel has also beefed up security across the country, sending hundreds of soldiers to back up thousands of police officers. Police have erected concrete barriers and checkpoints at the entrance to Arab areas of East Jerusalem, where many of the attackers are from.

Ten Israelis have been killed over the last month, mainly in stabbing attacks. On the Palestinian side, 48 people have been killed, 27 of them identified by Israel as attackers, the others killed in clashes with Israeli forces.

The Associated Press contributed to this report.