A spokesperson for Twitchsaid the video of the attack has been removed and the account it was posted from was suspended.
The killings took place on Yom Kippur, the holiest day of the calendar in Judaism, when Jews fast, seeking atonement.
After not being able to open the door to the Synagogue after several attempts, the attacker got into his auto.
"We unfortunately have to face the truth, which - for some time already - is that the threat of anti-Semitism, right-wing extremism, and right-wing terrorism is very high", Interior Minister Horst Seehofer told reporters on Thursday.
"It is scandalous that the synagogue in Halle is not protected by police on a holiday like Yom Kippur", he said. Unable to enter the synagogue, he shot one woman before driving to a kebab shop where he shot another person.
Without mentioning the far-right Alternative for Germany (AfD) by name, Merkel and Steinmeier condemned xenophobic rhetoric they said had grown increasingly mainstream and unsafe. It said investigators also have a video that the assailant apparently filmed with a camera on his helmet.
Police have detained one suspect and believe that the German man acted alone in this heinous act. They didn't specify why the "acute" danger is now deemed to have passed.
Once he had committed the crime, he attempted to flee but was quickly caught up in a shooting match with the police.
Spokesman Hana Rubasova says officers are focusing on synagogues and other Jewish buildings and objects, Prague's global airport and the border.
Police said in a tweet that the suspects fled in a vehicle, and soon after reported that one person had been arrested. "They have taken over the investigations". Prosecutors will have to sift through his communications and his activities on the darknet, a part of the internet hidden from public view.
"According to the federal prosecutor there are sufficient indications for a possible right-wing extremist motive".
Police union head Oliver Malchow said the response time showed "how thin police coverage is", and added that the wait "was especially long for the people who were in the synagogue".
While many questions remain about the suspect, German officials sought to reassure a shaken Jewish community after Wednesday's attack in the eastern city of Halle.
The clip shown by regional public broadcaster MDR shows the man getting out of a auto and firing four shots from behind the vehicle from a long-barrelled gun. It wasn't clear what he was shooting at. At least two other people were reportedly injured.
The man was later seen shooting at a patron of a kebab shop about 600 metres (yards) away from the synagogue. It also said the number of far-right extremists rose by 100 to 24,100 people previous year, with more than half of them considered potentially violent.
The suspected gunman was later arrested, a police spokesman confirmed Wednesday.
The Daily Mail quoted one worshiper, identified only as "Roman R." as saying, "We barricaded the door to the prayer room with chairs" during the attack. The Bild and Mitteldeutsche Zeitung newspapers reported the shooting took place near a synagogue.
Police didn't give any further information, but said officers were out in force in the city hunting down the suspects. Researchers told the Jewish Telegraphic Agency that the German method of categorizing the attacks is flawed: They cited, for example, a synagogue arson attempt by three Palestinians in 2014 that was not deemed anti-Semitic.
Fears of a new Islamist attack were also revived on Monday when a Syrian man hijacked a articulated lorry and smashed it into cars stopped at a traffic light in the city of Limburg, injuring several people.