The building has been sealed off and staff evacuated.
Jordan said he can only leave the country after an investigation.
Protests have since broken out in the holy site, with dozens of Muslim worshippers refused to enter the Mosque and prayed outside, considering the security checks a "violation" of the third holiest place for Muslims.
One of the Jordanians killed was a physician at the scene, the security agency said.
The incident is bound to further inflame Jordanian public opinion against Israel and complicate efforts to defuse tensions over a contested Jerusalem shrine.
Israel's Foreign Ministry said the incident began when two Jordanian workmen arrived at the building to replace furniture.
Both Ziv and Israel's ambassador to Jordan were invited to the Prime Minister Benjamin Netanyahu's office shortly after their release."I am happy to see you, happy that things ended as they ended, you acted in a cool, collected manner, and we had a commitment to take you out, it was not a question at all", the Prime Minister said.
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Priebus also affirmed his commitment to Trump's presidency, noting that he was "always going to be a Trump fan". Even before joining Trump's cabinet as secretary of Homeland Security, Kelly was Trumpian in his own way.
Security cameras have now also been installed at a gateway leading to the site.
One of the workers allegedly stabbed an Israeli security officer with a screwdriver, who, in self-defence, opened fire on the assailant, 17, reports Efe news. The tensions have led to mass prayer protests and deadly Israeli-Palestinian violence.
Another Jordanian, identified as the owner of the building, was injured in the gunfire and later succumbed to his wounds at the hospital. The cameras would be installed in Jerusalem's Old City where the shrine is located.
Three people were initially wounded in the incident, the security agency said.
Israel's security Cabinet met from late Sunday until the early hours of Monday to discuss the crisis at the shrine and the embassy shooting, and convened again Monday evening. On Monday, there were growing signs Israel was testing alternative security arrangement. Such railings are typically used for crowd control, to create orderly lines.
A spokesman for Israel Police has been contacted for comment.
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