The attack in July has led to a rift between two the neighboring countries.
Jordan said Israel apology was asked for and granted. Embassy in Amman to reopen.
It is in the vital interests of both countries that Israeli-Jordanian relations be put back on track.
Jordan refuses to allow Israel's ambassador to return to Amman unless the security guard who shot dead two Jordanians is investigated and tried.
“This assistance has never encouraged terrorism, the opposite is true” says Palestinian head of the commission for detainees Issa Qaraqe.
Israel says the guard fired in self-defense after being stabbed by a screwdriver-wielding Jordanian workman.
"With Jordan we have to walk very carefully and be aware of the sensitivity of the relationship and the status of Jordan in the Arab world.”
The Jordanian paper noted that, according to documents obtained, the guard carried a diplomatic identity card.
A heavy Jordanian police presence had sealed off the area around the embassy so the protesters gathered nearby.
The incident at the embassy in Amman this week is emblematic of Israel’s wider problem in the Middle East.