During that period, Israeli forces have killed more than 255 Palestinians, mostly attackers.
Local media report that one of the Jordanians, who allegedly worked for a furniture company engaged at the embassy compound, stabbed the Israeli citizen before the pair was shot dead by security. Authorities in Amman have refused to allow the guard to leave, insisting that they want to question the security officer, but Israel claims he is protected from arrest and investigation.
The Israeli embassy is located in the posh Rabiyeh neighbourhood in Amman.
The row has complicated the foreign ministry's efforts to evacuate the embassy.
The Jordanians had entered an apartment building in the compound to perform carpentry work, the statement said. "The first Jordanian, 17-year-old Mohammed Jawawdeh, succumbed to his injuries at the scene". Some details of the incident and security guard's name are still subject to a gag order.
Pope Francis said yesterday he was alarmed by the recent violence in Jerusalem and called for dialogue and moderation to help restore peace, reported Reuters. He says his son was unaffiliated with any group.
The Foreign Ministry said the security officer has diplomatic immunity from "investigation and imprisonment", according to the Vienna Convention.
Israel reopened the compound on July 16, but with metal detectors and surveillance cameras put up at entrances.
The lawyer is briefing Muslim leaders Monday. Jordan and Israel have close security ties, but frequently clash over Israeli policies at the Jerusalem shrine.
In a sign of the importance Israel places on its ties with Jordan, the Israeli government moved quickly to restore calm.
The embassy has always been a focus of anti-Israeli protests during times of Israeli-Palestinian friction, according to Reuters.
The drama played out as President Donald Trump's Mideast envoy, Jason Greenblatt, headed to the Holy Land on Monday.
Israel implemented the Temple Mount security measures following a terror attack 11 days ago, in which three Israeli Arabs attacked and killed two border policemen with weapons that had been hidden on the Temple Mount. The tensions have led to mass prayer protests and deadly Israeli-Palestinian violence.
Israel has said the metal detectors were a needed security measure to prevent future attacks.
Earlier reports said that one person had died and two - including one Israeli - were injured in Sunday's incident in a residential building used by embassy staff. Jews consider the same site their holiest, where the ancient Temple of Solomon once stood.