It was not immediately clear whether the incident in Amman -- in which a Jordanian man was killed and an Israeli seriously injured -- was linked to the dispute over the Jerusalem compound.
But it came after new security measures were implemented at the Jerusalem holy site after a weekend of violence left eight people dead, with fears of further violence.
Israeli officials signalled they may be open to changing the measures at the Haram la-Sharif mosque compound, known to Jews as the Temple Mount, after metal detectors were installed at entrances following an attack that killed two policemen.
Jordan is the custodian of the holy site, and in what a security source in Amman described as an "incident" at the Israeli embassy Sunday, a Jordanian man was killed and an Israeli seriously injured.
Police in Amman said there had been "a shooting at a residential building inside the compound of the Israeli embassy".
"An initial investigation indicated that three people were wounded, one an Israeli who was taken to hospital," a statement said, adding that two Jordanians were wounded and one later died of his injuries.
An investigation into the shooting was under way.
Israel and Jordan are bound by a 1994 peace treaty, but tensions have been high over the new security measures at the sensitive Jerusalem site in annexed east Jerusalem.
The metal detectors remained in place on Sunday, though cameras had also been mounted near at least one entrance to the compound in Jerusalem's Old City -- a possible indication of an alternative.
Tensions have risen following the July 14 attack that killed two policemen.
Israeli authorities say the attackers smuggled guns into the site and emerged from it to shoot the officers.
An investigation into the shooting was under way.
Israel and Jordan are bound by a 1994 peace treaty, but tensions have been high over the new security measures at the sensitive Jerusalem site in annexed east Jerusalem.
The metal detectors remained in place on Sunday, though cameras had also been mounted near at least one entrance to the compound in Jerusalem's Old City -- a possible indication of an alternative.
Tensions have risen following the July 14 attack that killed two policemen.
Israeli authorities say the attackers smuggled guns into the site and emerged from it to shoot the officers.
House set for demolition
On Friday evening, a Palestinian broke into a home in a Jewish settlement in the West Bank during a Sabbath dinner and stabbed four Israelis, killing three.
The Israeli army said the 19-year-old Palestinian had spoken in a Face book post of the holy site and of dying as a martyr.
On Saturday, Palestinian youths hurled stones and petrol bombs as the army used a bulldozer to close off the attacker's West Bank village and prepare his house for demolition.
Netanyahu said Sunday the demolition would go ahead "as soon as possible".
Israel frequently razes or seals attackers' homes as a deterrent, although rights groups say this amounts to collective punishment.
Clashes also flared in east Jerusalem and other Palestinian villages in the West Bank near Jerusalem on Saturday, police said.
Two Palestinians died, including one when a petrol bomb exploded prematurely.
Israeli security forces said Sunday they had arrested 25 men active in the militant Hamas group that rules the Gaza Strip.
Rocket fired from Gaza
Also Sunday, a rocket fired at Israel from Gaza hit an open area, the army said, causing no injuries. No group claimed the attack.
The holy site in Jerusalem has served as a rallying cry for Palestinians.
In 2000, then Israeli opposition leader Ariel Sharon's visit to the compound helped ignite the second Palestinian intifada, or uprising, which lasted more than four years.
The Haram la-Sharif/Temple Mount is in east Jerusalem, seized by Israel in the 1967 Six-Day War and later annexed in a move never recognised by the international community.
Considered the third holiest site in Islam, it is the most sacred for Jews.
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