Abdullah II called on Netanyahu to "take responsibility and take legal steps including the trial of the killer", he said, quoted in a royal court statement.
Jordan allowed the security guard to go home to Israel on Monday after he was held for questioning over the previous night's shooting.
The guard was welcomed home and greeted as a hero by Netanyahu, who embraced him and said: "You acted well, calmly and we also had an obligation to get you out."
The king called on the Israeli premier to "implement justice instead of dealing with this crime in the manner of a political show for personal political gains".
"This kind of behaviour -- which is unacceptable and provocative on all levels -- has made us all angry... And feeds extremism in the region," he said.
He vowed Jordan would do everything possible towards obtaining justice for its two slain nationals.
Israel's foreign ministry said the security guard shot dead a Jordanian worker who had come to an apartment to install furniture and had stabbed him in the back with a screwdriver.
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.
Jordan is the official custodian of Muslim holy sites in Jerusalem, but it remained unclear if the incident was linked.
Israel and Jordan signed a peace treaty in 1994.
Jordan's public prosecutor said today he had concluded his investigation into the embassy deaths, the official Petra news agency reported.
However, Musaid said in comments carried by Petra: "It became clear to the public prosecution through the investigation that the killer enjoys diplomatic and judicial immunity", and he had decided to drop the case.
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