The shooting, in which an Israeli security guard killed two Jordanians after being attacked by one of them with a screwdriver, came as a United States envoy headed to the region to try to defuse the crisis over the shrine.
A Jordanian government source, who declined to be named, said Tel Aviv was "still examining the request" to quiz the guard involved in Sunday's incident, which according to Israeli officials saw a Jordanian attack the guard with a screwdriver.
They said in a statement they were "informed late evening (Sunday) of a shooting at a residential building inside the compound of the Israeli embassy". Jordanian police said the building owner was a physician.
Israeli media said Jordan has demanded to conduct an investigation and has prevented Israeli embassy staff from leaving the premises.
Jordan is the official custodian of Muslim holy sites in Jerusalem. The security officer, the Jordanian landlord and two Jordanian workers were present.
Argaman reportedly reconstructed the attack with the Jordanians and produced evidence that the attacker - Mohammed Zakaria al-Jawawdeh, 17 - had a record of violent behavior, which cleared away any remaining doubts that the guard's account was true.More news: Three Israelis stabbed to death in West Bank settlement: army
The guard opened fire, killing the teen, the media reports said.
On Friday last, July 21, following calls from left-wing groups and Muslim integralists, thousands of Jordanians demonstrated in front of the Israeli embassy against the installation of metal detectors and cameras for entry onto Temple Mount in Old Jerusalem.
"The government is under pressure by deputies because it allowed the Israeli killer to leave", he said, stressing that the decision had to be taken in this way out of Jordan's commitments to global conventions.
The incident came at a time of heightened tension in the region over a Jerusalem holy site. The Israeli was in "unstable" condition, reported news site Hala Akhbar, linked to the Jordanian military.
Muslim religious leaders have alleged that Israel is trying to expand its control at the site under the guise of security, a claim Israel denies.
The embassy has been a meeting point for protests regarding turmoil in the Palestinian territories.
"I am happy to see you here and that things ended the way they did", Netanyahu said.