Jordan said Monday it was looking to question an Israeli security guard who killed two Jordanians at the Amman embassy compound, as Israel insisted he had diplomatic immunity.
A Jordanian government source said Israel was "still examining the request" to quiz the guard involved in Sunday's incident at an annex building in the Israeli embassy compound.
Amman says two Jordanians, one of them a teenager, were killed in a shooting and an Israeli stabbed and wounded.
"The first Jordanian, 17-year-old Mohammed Jawawdeh, succumbed to his injuries at the scene," a Jordanian security source said.
"The second, Bashar Hamarneh, a doctor who was in the residential quarter of the embassy at the time of the incident... died of his injuries after midnight in hospital," the source added.
He was apparently shot by accident.
The injured Israeli is "deputy director of security at the Israeli embassy and is still receiving treatment in hospital", said the source.
Israel's foreign ministry said that Jawawdeh, who had gone to the compound to install furniture, had stabbed the security guard in the back with a screwdriver.
"Jordan has requested to question the Israeli embassy security guard... (and) Israel is still examining the request," the Jordanian government source, who declined to be named, told AFP.
The source said Jordan is "fully aware of international agreements concerning this case and understands them completely but is seeking Israel's cooperation".
"There is no need for a diplomatic escalation," he said.
Israel's foreign ministry said "in accordance with the Vienna Convention, the security officer has immunity from investigation and imprisonment".
"Prime Minister Benjamin Netanyahu spoke with Eynat Schlein, Israel's ambassador to Jordan, and with the security official," a spokesman for the ministry said.
"The (Israeli) ministry of foreign affairs and security authorities are working with the Jordanian government over various channels," the spokesman added.
Jawawdeh's father, Zakariya Jawawdah, told AFP he wanted "the truth", urging authorities to view CCTV footage from security cameras at the embassy.
"My son has no interest in politics. He does not follow any extremist ideology," he said.
The government spokesman said an initial investigation indicated that Jawawdeh and the security guard "fell out over some dispute which led to a stabbing and a shooting". Israel and Jordan are bound by a 1994 peace treaty.
But tensions have been high in recent days after Israel put in place security measures at the highly sensitive Al-Haram Al-Sharif mosque compound in east Jerusalem, known to Jews as Temple Mount.
Israel installed metal detectors at entrances to the site following an attack nearby on July 14 that killed two of its policemen.
Palestinians view the move as Israel asserting further control over the compound, home to Al-Aqsa mosque and Dome of the Rock, and considered Islam's third holiest site.
Jordan is the official custodian of Muslim holy sites in Jerusalem.
Israeli measures at the flashpoint site sparked angry demonstrations in Amman on Friday, when thousands took to the streets in a protest called by Islamist movements and leftist parties.