On Monday, Mrs McAleese said the centre had diminished the name of Simon Wiesenthal -- the famed Nazi-hunter -- in its dealings with the Hunt Museum in Limerick.
Mrs McAleese smiled for reporters, but did not speak about the ongoing row, as she was given an honorary fellowship by City and Guilds.
The previous night, controversy had flared when the president visited the Hunt Museum during a visit to Limerick. She had spoken about allegations made against the museum by Dr Shimon Samuels, director of the Paris-based Simon Wiesenthal Centre Europe. Dr Samuels asserted that the museum-found John and Gertrude Hunt had traded with "notorious dealers of art looted by the Nazis".
However, a report by Dr Lynn Nicholas, a world authority on artwork stolen during the Second World War by members of the German army, later found no proof that the Hunts were Nazis or that they were "traffickers in looted art".
Revisiting the controversy this week, Mrs McAleese said that, growing up, the name of Simon Wiesenthal was a name she deeply respected. But she could not say the same about the Simon Wiesenthal Centre, which she said had diminished his name in a way it had dealt with the Hunt museum.
Mrs McAleese added she was saddened by the fact that the late John Hunt had gone to his grave not knowing that the museum would later be vindicated in a report.
Yesterday her press office said she would be saying nothing further on the matter. But Dr Samuels said her remarks were "uncalled for". He said the provenance of the Hunt collection had not yet been proven and that the centre would publish its own report in the next three months.
Meanwhile, Mrs McAleese paid tribute to City and Guilds, the vocational education and training body, at the ceremony in Dublin yesterday morning.