Speaking in English, the man called himself "anon" and said he was a Holocaust denier.
“Feminism is the cause of declining birth rates in the West, which acts as a scapegoat for mass immigration, and the root of all these problems is the Jew,” he continued, while filming himself in a car before starting the attack.
The 35-minute livestream was verified by the International Centre for the Study of Radicalisation (ICSR) at King's College London after being shared online.
Police said at least two people had been killed in Halle - outside the synagogue and at a nearby kebab shop - and a separate shooting was reported in a nearby town later on Wednesday.
The attack started at around noon local time (11am BST) on Humboldtstrasse, which houses the synagogue and Jewish cemetery.
Witnesses reported that a gunman, wearing a helmet mounted with a camera and military-style clothing, attempted to storm the synagogue and then shot a female passerby.
The headcam footage showed the attacker spending several minutes attempting to break into the synagogue, and swearing in German repeatedly as he failed.
He opened fire at a gate in its perimeter wall and threw homemade grenades into the neighbouring Jewish cemetery.
The attack came during Yom Kippur, a Jewish religious festival that sees observers fast and pray to atone for sins.
A spokesperson for the local Jewish community said that up to 80 worshippers were inside the synagogue at the time, but security measures at its entrance “withstood the attack”.
The footage showed a female passerby shouting at the gunman as she walked past, before he shot her multiple times in the back.
Several other people seen in the video, including an elderly cyclist and passing motorists and pedestrians, were spared.
"Sorry guys ... one time loser always a loser," the gunman said as he drove away down a road that led to a junction facing a kebab shop.
The livestream showed him getting out of his car and approaching the takeaway, then throwing a homemade grenade as the people inside ran into the back.
Later on Wednesday, a written manifesto emerged online where the shooter published photos of the homemade gun, pipe bombs and grenades used in the assault.
He claimed he had initially planned to target a mosque or culture centre, where he believed "antifa" would be present.
Survivor Conrad Roessler told N-TV: “All the customers next to me ran ... I locked myself quietly in this toilet, and wrote to my family that I love them, and waited for something to happen.”
The gunman appeared to have problems with what he called an "improvised weapon" jamming and cursed repeatedly, before shooting a man hiding behind a drinks fridge at point-blank range.
The livestream showed him leaving the takeaway and opening fire at vehicles in the street, before returning to the kebab shop and shooting the same victim several times.
He then stopped his car in the road and appeared to fire randomly over its roof towards motorists, before driving away.
"I’m a complete loser," the attacker said, then disappeared after apparently discarding the camera and dumping his Volkswagen Golf.
One victim's body was in the street outside the synagogue, while another victim was found inside the Turkish kebab shop.
Officials at the Uniklinikums Halle hospital said it was treating two more people for gunshot injuries, including a victim undergoing surgery.
A separate shooting was later reported in the town of Landsberg, around a 20 minute drive from Halle.
Anja Werner, the mayor of Landsberg, later said a car had been hijacked and driven onto a motorway that leads to Munich.
Halle's main railway station was shut as the search operation continued, and Germany's federal police were increasing controls at land borders and airports to prevent any potential escape.
Investigators said they had arrested one person following the attack, but it was unclear whether other suspects could be at large.
The country’s federal public prosecutor has taken over the investigation into the case - a move commonly seen for suspected terror attacks.
Before the Twitch footage emerged, a spokesperson told The Independent they were looking into potential ideological motivations including far-right extremism, but had not confirmed the background to the shootings.
The footage has since been removed from the Twitch website, which focuses on video game streaming, but was still being spread online.
A live broadcast was also made by the Christchurch shooter, who used Facebook Live, and posted a “manifesto” espousing a theory that white people are being eradicated from Western nations on the 8chan image board.
On the 4chan website, some posters were comparing the Halle shooter to “Saint [Brenton] Tarrant”, while another wrote: “Kill society, one lone gunman at a time. F***, I’m lovin it.”
Others ridiculed the shooter, who called himself a “loser” repeatedly in the video, for failing to kill more victims.
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