The Jewish Representative Council of Ireland has said it is "disappointing" that Sinn Féin leader Mary Lou McDonald has yet to condemn "offensive comments" by Réada Cronin.
The newly elected Kildare North TD made a number of controversial remarks on Twitter when she was a councillor.
She posted remarks about Israel and staff at the Israeli embassy, as well as making derogatory comments about judges.
Chair of the council Maurice Cohen said the tweets were "inaccurate, anti-Semitic and racist".
He said Ms Cronin's comments were based on a lack of knowledge.
"A little education on what constitutes anti-semitism would go a long way to correcting this problem," he said.
Ms Cronin's Twitter account has been made private since the tweets emerged.
She has issued a statement in which she "unreservedly and wholeheartedly" apologised and said the tweets were "glib" and "off-the-cuff".
Earlier, Sinn Féin's Pearse Doherty said the comments made by Ms Cronin were not a reflection of the party's positions.
He said he had not seen the comments, but said she had withdrawn them and apologised, which he said was the right thing to do.
Mr Doherty, who is leading Sinn Féin negotiations on government formation, said he did not believe the comments would have implications on talks with other parties, which he said were about "serious substantive issue" around health and housing.
Asked if he believed there was a latent ambivalence about the comments within the party, he said: "No, there is not."
Sinn Féin's Pearse Doherty has said that social media comments made by newly elected Kildare North TD Réada Cronin are not a reflection of the party's positions | Read more: https://t.co/YfLiyUa6bL pic.twitter.com/uaxKtA6mlt— RTÉ News (@rtenews) February 19, 2020
Mr Cohen urged Sinn Féin and the other political parties "to adopt the International Holocaust Remembrance Alliance (IHRA) working definition of Anti-Semitism.
"The definition has been adopted by most countries in Europe and as Ireland is already a signatory to the IHRA we have de facto accepted it.
"It is now up to our politicians to adhere to it."
Additional reporting: Mary Regan, PA