On Friday thousands of people gathered in Amman protesting at the security measures.
A Jordanian security source named the first dead man as 17-year-old Mohammed Jawawdeh and the second as Bashar Hamarneh, a doctor who was in the residential quarter of the embassy at the time of the incident.
"In accordance with the Vienna Convention, the security officer has immunity from investigation and imprisonment", said Emmanuel Nahshon, a foreign ministry spokesman.
An investigation into the shooting was still underway, the police said.
The detectors were installed after two Israeli policemen were shot dead by three Arab-Israeli gunmen on July 14. Palestinians allege they are an Israeli attempt to control the site and have launched mass protests.
"The Israeli government is playing with fire and risking a major crisis with the Arab and Islamic world".
The security guard was lightly wounded, the foreign ministry statement said. Netanyahu said that the government was "carrying out discussions at all levels with security officials in Israel and the government in Amman in order to bring this situation to a resolution".
One Jordanian was killed, another wounded and an Israeli was seriously wounded at Israel's embassy in Amman, a police statement said. His father told Jordanian media Monday that as far as he was concerned, his son was a "martyr", and that the only possible punishment was the death penalty.
The tourists were in Jordan to visit the Tomb of Aaron، the biblical high priest and brother of Moses، who tradition holds is buried on Mount Hor، near Petra، at a site known locally as Jabal Haroun.
"Since the start of the events, I have held a series of assessments with security elements including those in the field", Israeli Prime Minister Benjamin Netanyahu said at the start of Sunday's cabinet meeting. It says they are meant to prevent more attacks.
Jordan is the custodian of the Al-Aqsa complex and has a large Palestinian population, making Amman sensitive to any changes of status at the site which Israel captured along with other East Jerusalem and West Bank areas in the 1967 war.
Around half of Jordan's seven million citizens are of Palestinian origin.