The shooting has drawn comparisons to the death of George Floyd in the US and prompted a series of small demonstrations against police violence toward Palestinians. Some Israeli figures have paid condolence visits to the grieving Hallaq family.
At last week's Cabinet meeting, a day after the shooting, Defence Minister Benny Gantz, who is also Israel's "alternate" prime minister under a power-sharing deal, apologised for the incident. Mr Netanyahu, seated next to him, made no mention of it in his remarks at the time.
"What happened with the Hallaq family, with Eyad Hallaq, is a tragedy. A person with disabilities, with autism, who was suspected we now know unjustly of being a terrorist in a very sensitive place," Mr Netanyahu said Sunday. "We all share in the grief of the family."
Mr Netanyahu said he was awaiting police examinations of the event, but unlike Mr Gantz did not apologise. Israel's Justice Ministry has said two officers have been placed under house arrest, but gave no further details.
Police said that officers in the Old City spotted a man carrying a "suspicious object that looked like a pistol." When the man failed to heed calls to stop, police said they opened fire and "neutralised" him after a chase in a volatile area that has seen several previous attacks.
For Palestinians in the occupied West Bank and contested east Jerusalem, and members of Israel's Arab minority, these cases reflect what they see as Israeli forces' loose trigger fingers when it comes to dealing with Arab suspects.
Mr Hallaq's death, in particular, has reverberated across Israel, with his image raised on signs at a demonstration in Tel Aviv Saturday night against Israeli plans to annex parts of the West Bank. "This is what occupation looks like," read signs bearing Hallaq's image.
Inspired by the protests in the US, demonstrators held signs reading "Palestinian Lives Matter" and photographs of Hallaq alongside Mr Floyd.