Shaare Zedek Hospital announced that the man, who was evacuated there in serious condition, is now moderate and stable.
Earlier on Wednesday, Israel's emergency medical response service, Magen David Adom (MDA), reported that two people had been wounded as a result of the attack.
The attempted terrorist rushed towards Border Police officers with a knife but was shot before he could harm any of them.
The incident comes after New South Wales police last month charged several boys with terrorism-related offenses in investigations following the stabbing of an Assyrian Christian bishop.
The terrorist who carried out the attack was identified as a 34-year-old Turkish citizen.
Two members of the public and two police officers were in the hospital with non-life-threatening wounds.
The terrorist has been neutralized by a civilian, according to Maariv, and an additional suspect was captured nearby.
Alid had first used two knives to attack his sleeping housemate, to whom became aggressive after learning of his conversion to Christianity, stabbing him six times while shouting "Allahu Akbar."
One terrorist attempted to stab IDF soldiers, while a second terrorist shot at soldiers from Palestinian territory, Israeli media reported.
Police from the joint counter terrorism team questioned the boy, who is in a hospital under police guard recovering from injuries.