An attack on one Jew is an attack on all, said Fagin, adding that "our prayers and thoughts are with our brethren in Halle".
"In my youth, there was a threat of anti-Semitism from left-wing and Islamic terrorism", said Munich resident Daniel Targownik, 53, the son of a Polish Holocaust survivor and his Israeli wife.
German chancellor Angela Merkel joined a vigil held at Berlin's New Synagogue after the attack.
By that point, the suspect had already shot a woman in the street and a man at a nearby kebab shop. He is now in custody. Prosecutors will have to sift through his communications and his activities on the darknet, a part of the internet hidden from public view.
The suspect in an attack on a German synagogue on Judaism's holiest day had around four kilograms (nearly nine pounds) of explosives in his auto and wanted to carry out a massacre, Germany's top prosecutor said.
Orthodox Union executive vice president Allen Fagin said in a statement that this "senseless act of anti-Semitic violence was not only a heinous attack on the Jewish community of Halle, but ... yet another example of anti-Semitism in Germany, which continues to proliferate". While the Christchurch shooter wanted to kill as many Muslims as possible, he also had secondary and tertiary aims: for New Zealand and the United States to ban guns (the reaction), causing people to rise up (the counter-reaction).
He called the attack "a disgrace for our whole country".
Yet the right-wing threat is a new phenomenon, and especially risky given Germany's history, said Targownik. He added: "We all have to fight against anti-Semitism in our country".
"They have taken over the investigations".
Before he began shooting on October 9, the attacker also broadcast an anti-Semitic manifesto online.
The synagogue in Halle - a city of less than 300,000 people - has technological security measures but no permanent guard around the close, Max Privorozki, the head of the Jewish community in Halle said in video on Twitter. We must learn from this incident to make sure that nothing similar ever happens again.
"Our solidarity is with Germany's Jews on this Yom Kippur".
"Mr. President, I feel your pain, concern and fear and I share it. I don't want our society to lose that", said the 65-year-old from Halle, who said he was a practising Catholic.
Proponents of replacement theory, such as the Identitarians, a more mainstream far-right group who say European "identity" risks being extinguished by mass immigration, were at pains to distance themselves from the perpetrator within hours of the shooting.
Amazon-owned Twitch recently hosted the livestream of the recent shooting in Germany, where the shooter streamed his attack live with 2200 viewers, but Twitch were quick to remove the stream in 30 minutes.
"It is not enough to condemn such a cowardly attack", he said.
"We share in the mourning of the families whose loved ones were murdered, wish the wounded a speedy recovery and send strength to the worshipers and members of the community who are in deep mourning", he said. "Those who so far have been silent must speak out".
Police enter a Jewish cemetery over a wall near the scene of the shooting.
The former communist states in east Germany have also gained notoriety for their far-right extremists. At one point, the apparent shooter looked into the camera and recited an antisemitic screed in which he denied the Holocaust occurred.
Mr Luebcke's killing has deeply shaken Germany, raising questions about whether it has failed to take seriously a rising threat from right-wing extremists.