Defense Minister Benny Gantz met Tuesday with Jordan's King Abdullah II at his palace in Amman to discuss "regional security challenges" ahead of Ramadan.
According to official sources who spoke to Reuters later that day, President Isaac Herzog will also hold talks with King Abdullah in Jordan on Wednesday.
Gantz's visit was planned before the Islamic State-linked attack that killed two Israelis in Hadera Sunday.
According to the Defense Ministry, Gantz presented the King with Israel's plan to preserve freedom of worship in Jerusalem, and emphasized the "importance of security coordination" in light of recent events. The meeting was attended by Jordanian Foreign Minister Ayman al-Safdi and intelligence chief Maj. Gen. Ahmad Husni.
A statement from the Jordanian royal palace said that the king emphasized to Gantz "the need to keep the complete calm and respect the rights of Muslims to plat at al-Aqsa Mosque, and to remove every obstacle ahead of them and to avoid any skirmishes that could lead to an escalation."
The statement added that King Abdullah also discussed the need to increase efforts to renew an effective negotiation process between Israelis and Palestinians "that would ensure the establishment of a Palestinian state within the 1967 borders, with East Jerusalem as its capital."
Israel's Public Security Minister Omer Bar-Lev also met last week with al-Safdi in Amman to discuss the threat of escalation as part of Jordan's efforts to cool tensions leading up to the holy month.
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With the holidays coinciding with Passover this year, the Shin Bet and Israeli police are gearing up for violent confrontations, particularly in Jerusalem.
Abdullah also met with Palestinian President Mahmoud Abbas in Ramallah on Monday, after skirting an unofficial invitation to an Israeli summit for its Middle Eastern allies. Palestinian Prime Minister Mohammad Shtayyeh dubbed the summit "one big illusion."
Following his meeting with Abbas, Abdullah called on Israel to "freeze all unilateral measures, especially in Jerusalem and the al-Aqsa mosque, that hinder a regional settlement and the establishment of a Palestinian state."
He emphasized the need to "maintain the status quo" across holy sites in order to prevent violent confrontations, and affirmed support for the Palestinian cause.
"We and the Palestinians are on the same side of the barricade," the king said. "We arrived in Ramallah today to hear what the Palestinians are demanding and to reduce the obstacles and challenges they face."
On Monday, Prime Minister Naftali Bennett said that he had ordered a bolstering of Israel's security forces until Independence Day on May 5, with an emphasis on volatile regions at risk of violence following a terror attack that left two Israelis dead and put Israel's security echelon on high alert.
Security forces intend to conduct a large-scale arrest operation against individuals suspected of involvement in terrorism and to detain them without charges. Defense officials have begun drawing up a list of Israeli Arabs to arrest based on purported information about involvement with terrorism, and plan to conduct a thorough investigation of social media networks to identify those calling for violence.
Earlier this month, Foreign Minister Yair Lapid met with King Abdullah II also to "quell tensions and promote understanding," ahead of the holidays, a statement from Lapid said.
Reuters contributed to this report.