He married school teacher Lorraine 10 days ago and the pair went on honeymoon to a number of destinations in Europe.
But there was anger today when Cllr O'Neill posted pictures on his Facebook page of his wife standing beside a waxwork dummy of Adolf Hitler at a museum in Rome and giving a Nazi salute.
Mrs O'Neill can also be seen making a "rabbit" gesture behind the Hitler dummy's head.
When asked about the pictures, Cllr O'Neill, who works on RTE's Sunday Sport programme, said: "The pictures are private. It was only a bit of fun." He refused to make any further comment. However the offending picture was removed from his Facebook page an hour later.
Yanky Fachlar, spokesman for the Jewish Representative Council in Ireland and organiser of the annual Holocaust Memorial Day at Dublin's Mansion House, said the picture was "deeply offensive".
He called on Fine Gael to raise the matter with the councillor.
"This sort of thing is highly insensitive and shows an incredible ignorance of Hitler and the Nazis.
"That salute and what it stands for led to the deaths of millions of people including some of my relatives.
"It beggars belief that there are some ignorant people like this who think it's fun, but especially someone who was elected as a councillor and his wife," he said.
Mr Fachlar, whose friends helped to save hundreds of Jews during the war in and around Rome, said he was "astonished" the museum had such an exhibition.
"This is something to raise with the Jewish community there," he said.
Online 'friends' of the councillor, who comes from Ballyshannon in Co Donegal, expressed shock at the images. One of them said: "I was shocked to see the wife of an elected councillor posting pictures of herself giving the Nazi salute.
"To simply adopt this gesture is illegal in Germany and Austria and I am personally offended beyond words as I lost ancestors to the Hitler regime."
Cllr O'Neill married schoolteacher Lorraine McCabe on December 30. More than 500 guests attended a reception at the Abbey Hotel in Donegal Town. The couple then flew off for a tour of Europe, spending several days in Rome. Cllr O'Neill is well-known in music circles as the main organiser of the annual Rory Gallagher Music Festival.