As Israeli police's internal investigations department has opened a probe after the killing of a Palestinian man with mental disability by two Israeli police officers last week, Palestinians said they have little hope that it will result in any accountability.

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Iyad Hallaq, 32, was walking to his special needs school in the Old City of Jerusalem when he was called on to stop by Israeli forces.

The two policemen said in their official statement they suspected Hallaq was carrying a weapon and began chasing him when he panicked and ran to hide behind a dumpster, just a few meters from his school. There, the officers shot him dead.

A source within the investigation said one of the officers - a new recruit armed with an M16 assault rifle - is suspected of continuing to shoot at Hallaq despite being told by his commander to stop, according to Haaretz.

Hallaq was diagnosed with low-functioning autism as a child and had trouble communicating with people. According to his father, Khairy Hallaq, his son had the mental capacity of an eight-year-old - and no concept of the dangerous reality of life under occupation around him.

Hallaq was given special documentation by his school, which he had attended for the past six years, that explained his disability so he could prove his condition to Israeli forces, as he was unable to do so himself.

Israeli Minister of Defense Benny Gantz issued Sunday a rare apology.

"We are very sorry for this incident," Gantz said in a government meeting. "I am sure the issue will be investigated quickly, and conclusions will be drawn."

But Hallaq's cousin, Mansour Abu Wardieh, said the family is not optimistic about the police inquiry into the shooting.

"The news of Israeli authorities ordering an investigation into Iyad's murder means nothing to us," he told Al Jazeera. "We know they'll twist the facts and we won't be surprised if they concluded that the officers fired at him out of 'self-defense'."

Over the last decade, Israeli security forces have killed 3,408 Palestinians in the occupied Palestinian territories and within Israel, according to Israeli rights group B'Tselem.

But of these cases, only five Israeli security personnel including military and police were convicted.

"We don't have the number of investigations opened into police killings," B'Tselem media spokesperson Amit Gilutz told Al Jazeera. "But as far as the military goes, over this same period investigations into the killings of about 200 Palestinians were opened.