The Scottish Labour leader vowed to deal swiftly with the allegations including claims that Cllr Jim Dempster chased a six-year-old girl with an air freshener telling her that she “smelled like curry”.
Cllr Dempster had already been suspended by Labour for making a racially offensive remark about Transport Minister Humza Yousaf when the new allegations came to light.
Earlier this month Cllr Dempster apologised to Mr Yousaf for suggesting that if the minister had visited his council area “no-one would have seen him under the burka”.
The fresh accusations became public when two people, who wish to remain anonymous, approached Mr Yousaf and claimed they had been the victim of “disturbing abuse” when they were children around 30 years ago. Cllr Dempster denies the fresh allegations.
Cllr Dempster’s accusers are a brother and sister who grew up in one of the few ethnic minority families in the area. The sister said that when she was six or seven she was chased around the newsagent shop that the councillor used to run in Sanquhar, Dumfries and Galloway in the late 1980s and early 1990s.
The brother, who is slightly older, said he was subjected to “10-years of hell” at the hands of the local politician.
He said that when he was boy, Cllr Dempster would pick on him whenever he went into the shop, often referring to him as a “P**i”.
“He would also call me `Jew boy’ because he knew as Muslim I was circumcised, just as a Jewish person would have been. The racism I received from Jim haunted me my whole life. I tried to suppress it but I now feel I have to speak out.”
His sister said she had been called many names over the years including “chocolate monkey”.
She added: “When I was aged six or seven, Cllr Dempster chased me around his shop with an air freshener saying I smelled of curry.”
After First Minister’s Questions, Mr Leonard was asked if his party had a racism problem. The Scottish Labour leader replied: “We have got no more of a problem with racism than Scottish society as a whole but where these matters are brought to our attention, where we receive complaints we will investigate them thoroughly.”
He added: “I am impatient and I am angry that we are receiving complaints and they will need to be dealt with thoroughly and timeously. There will be zero tolerance of racism, Islamophobia inside the Scottish Labour Party.”
When asked how long the investigation would take, Mr Leonard said: “The investigation officer was appointed straight away and I believe contact has been made with him. It is my sincere hope that this can be dealt with rapidly, but it needs to be thorough and there needs to be due process, but it needs to be dealt with timeously.”
Mr Yousaf has called on Cllr Dempster to resign. Speaking on the Good Morning Scotland programme, the Transport Minister said: “It’s just really disturbing, these incidents took place allegedly a number of years ago but both victims tell me they really had just suppressed them but when they saw Jim Dempster’s face across the news they just said they had to come forward.
“They wish to remain anonymous but told quite graphic accounts of sustained racial abuse over a decade. One of the victims told me he was haunted by it, he said he had suppressed it, he said the 10 years that he lived in the area in Sanquhar and he was a victim of that abuse were the worst 10 years of his life.
“He said when he saw Jim Dempster’s face again on the news he couldn’t sleep. It really has had an impact on them, I really applaud them on their bravery having spoken to both of them.”