The incident is one of the most serious incidents between the two countries since they signed a peace treaty in 1994.
Reports said the owner of the residential building used by the embassy was hit with a stray bullet and killed. According to radio reports, Israel has dispatched a senior defense official to help resolve the crisis.
The incident happens on the background of the Jerusalem Temple Mount terrorist attack and the following massive manifestations against Israel in the West Bank, Gaza and some Arab world countries, including Jordan.
The embassy refused to turn the guard over to the Jordanians for questioning, saying he had immunity.
Jordanian security forces deployed in the streets around the embassy, an AFP correspondent said.
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.
But tensions have been high in recent days after Israel put in place security measures at the highly sensitive al-Aqsa Mosque compound in east Jerusalem, known to Jews as Temple Mount.
A police statement said the man was shot. The Jordanian landlord of the embassy compound was injured and later succumbed to his wounds, the ministry added.
Israel's ambassador to the United Nations said yesterday Israel is working to calm the situation in Jerusalem following a flare-up of violence, but it will do whatever is necessary to maintain security at a holy site.
Israel installed metal detectors at entrances to the site following an attack nearby that killed two policemen.
Netanyahu, who spoke with Ziv as well as Israeli Ambassador to Jordan Einat Shlain, said Israel had an "obligation" to get the two out of Amman and back to Israel.
President Abbas has suspended all contacts between the Palestinian Authority and the Israeli government on Friday in protest of the metal detectors. He said talks were under way whether to evacuate the embassy staff, given the tensions in Jordan.