The father of the teen assailant reportedly told a Jordanian television station that he does not believe his son meant to attack an Israeli.
Earlier in 1997, a Jordanian soldier opened fire at a group of Israeli schoolgirls on a field trip to a joint Israeli-Jordanian tourist resort along the border.
More details are awaited on the incident.
One Jordanian man was shot to death and an Israeli man was wounded after a fight at the Israeli embassy in Amman. Jordanian government officials were not immediately available for comment.
The son, a 17-year-old, stabbed the guard with a screwdriver late on Sunday. It said there was no Jordan proposal to trade the security guard for a removal of the metal detectors.
One Jordanian is reported to have been killed and two others wounded in a shooting incident at the Israeli embassy in Amman.
Monday's report in Hala Akhbar says Jordan wants to investigate the shooter and if Israel refuses to allow that, it will take "diplomatic measures".
No doubt this extremely serious event will complicate the already strained relationship between Jordan and Israel, entangled in sensitive regional negotiations to resolve the Jerusalem Temple Mount crisis and stabilize the situation.
Israeli measures at the flashpoint site sparked angry demonstrations in Amman on Friday, when thousands took to the streets in a protest.
The Israeli Embassy has refused to release the guard to the Jordanians for questioning, saying he has immunity.
Muslim authorities claimed the move is a way for Israel to expand its control over the site, something denied by Jerusalem, which said the decision aims to to prevent further violence.
However the MFA says that as a diplomat, the official is immune from "investigation or imprisonment" under global law. He spoke on condition of anonymity because he was not authorized to discuss the incident with the media.
The lawyer is briefing Muslim leaders Monday.
In another sign of the tense atmosphere, a Palestinian assailant stabbed an Arab citizen of Israel in the neck in central Israel, apparently mistaking him for a Jew, police said.
Israeli authorities say the attackers smuggled guns into the site and emerged from it to shoot the officers.
The detectors were installed after two Israeli policemen were shot dead by three Arab-Israeli gunmen on July 14.