The broadcaster has revealed that bosses are in close contact with Marty and are giving him time to "come to terms with his tragic loss”.
In a statement RTE said: “We were shocked and saddened to learn of the sudden passing of our colleague, Marty Morrissey's beloved mother, Peggy.
"We have been in touch with Marty to offer him our sincere condolences but also to offer him our support and to afford him the time and space to come to terms with his tragic loss.
"Our thoughts are with Marty and his family and close friends at this saddest of times."
The broadcaster's mum was killed in a single car collision in the early hours of the morning in Annagh in Miltown Malbay, Clare on Tuesday.
She was in her 90s.
Since the tragedy, tributes have been rolling in for Peggy, with people reaching out to Marty who is said to be distraught over the loss of his mum.
RTÉ sport journalist Darren Frehill said he knew Marty “meant the world” to his mother, as he passed on condolences to Morrissey on behalf of himself and his colleagues.
Speaking on RTÉ radio’s Rising Time programme, Frehill said that it was “desperately sad” and a “devastating loss”, adding that Peggy was “extremely popular” in her local community in Co Clare.
Rising Time presenter Shay Byrne said the show had received “hundreds of texts” from listeners in relation to Peggy’s death.
Fianna Fáil Clare TD Cathal Crowe offered his “very deepest sympathies” to the popular sports and entertainment presenter.
"Earlier this evening it was confirmed that the lady who tragically lost her life in last night’s road accident near Miltown Malbay was Peggy Morrissey, mum of the much-loved Marty Morrissey,” he tweeted.
“RIP Peggy, light of heaven to your soul. My very deepest sympathies to @MartyM_RTE."
Enda Rouane, sacristan at Peggy Morrissey's local church Our Lady Star of the Sea in Quilty, Co Clare, described her as “a lovely woman".
“Everyone around knew her and she was so well thought of.
“She was a very regular mass goer during the week and on Sunday. She was a Eucharistic minister.
“I think she was very proud of Marty, I’m sure she was. God rest her.”
Morrissey’s mother Peggy, whose maiden name was Twomey, was originally from Mallow, Co Cork, while his father Martin Morrissey came from Quilty in west Clare.
The sports presenter, who is an only child, lost his father on December 19, 2004.
In a recent interview with the Sunday Independent, the broadcaster described his father’s death as the saddest day of his life.
“He drove me to Shannon Airport from home. I said goodbye to him at departures,” he said.
His mother rang him when he arrived in New York to tell him the sad news and he said it was a “devastating blow” to the family.
Morrissey's parents left Ireland for New York as newlyweds in the early 1950s. There, his father set up a travel business, Morrissey Travel, in the Bronx.
Peggy, a former hairdresser, worked as a receptionist in a university.
When she became pregnant with Marty in 1958, she flew back to Ireland in order to have her baby in Cork. Marty was born at Mount Alvernia Hospital in Mallow.
Peggy returned to New York with her baby son one month later.
“She went back on one of those propeller planes for a 17-hour flight back to New York with me in her arms,” Marty said in recent years.
“It was some journey. She was brilliant, to be fair to her.”