However on the same programme, Holocaust survivor Susan Pollack called for Mr Corbyn to show leadership in tackling anti-Semitism.
In another message, the former MP, who stood down in 2010 wrote that "alleged anti-semitism" was "yet another stick with which to beat Corbyn - along with Corbyn 'friend of the IRA, Hizbollah, Hamas, Czech spy, Soviet spy..."
"When members of Jewish communities express genuine anxieties, we must recognize them as we would those of any other community", the opposition leader wrote on Facebook.
The organizations also held a demonstration outside parliament last month attended by various lawmakers, including prominent Labour MPs. "We welcome the fact that Mr Corbyn's words have changed but it is action by which the Jewish community will judge him and the Labour Party", they said.
Manson said while it was a "misery and tragedy" that some MPs had "received nasty anti-Semitic comments", there was no proof they had been made by Labour supporters, pushing the blame onto right-wingers.
Corbyn, however, described the meeting as "positive and constructive", and vowed to take further steps to combat the phenomenon. Jewish groups had said they would boycott it amid concerns about the inclusion of the pro-Corbyn group Jewish Voice for Labour.
Speaking after the meeting, JLC president Jonathan Goldstein said: "We are extremely disappointed that one month after we issued a very sensible and well-thought through series of proposals that not one of them have been given to the Jewish community".
Drug take-back event is Saturday
The drop-off location for this one-day event will be at the Milford Senior Center parking lot, 9 Jepson Drive, rain or shine. Last fall, 77 pounds of medicine was collected at MTSU collection events, said Lisa Schrader, director of Health Promotion.
The Labour leader is meeting with Jewish leaders to address concerns about how he has dealt with abuse and hostility.
But the groups said after the meeting that Corbyn failed to agree there should be a fixed timetable to deal with anti-Semitism cases or that no member of parliament should share a platform with somebody expelled or suspended for anti-Semitism.
Much of the fiercest criticism regarding Corbyn's leadership came from his own party's benches, particularly from Labour's Jewish parliamentarians.
They said Corbyn did not agree to any of their proposals during the Tuesday meeting. "And that of course goes for the Labour Party too". When calling for the protest, an open letter from the Board of Deputies and the Jewish Leadership Council accused Corbyn of siding with anti-Semites "again and again".
In his Evening Standard article, Mr Corbyn said that anti-Zionism was not in itself anti-Semitic but he acknowledged that "individuals on the fringes of the movement of solidarity with the Palestinian people can stray into anti-Semitic views".
In a statement issued on the day of the protest, Corbyn pledged to be "a militant opponent of anti-Semitism", telling the Jewish community: "In this fight, I am your ally and always will be".
Co-chair of the Jewish Voice for Labour Jenny Manson voiced these concerns during an interview with BBC Radio 4 on April 24 and added that most anti-Semitic comments made to MPs were done via social media, with numerous offenders using anonymous accounts.