The boy died following the traffic incident involving a car at a rest stop in Ennis, County Clare, on Wednesday afternoon.
The child was rushed to University Hospital Limerick after the incident at around 12.30pm but was later pronounced dead.
It has emerged that the boy's mother, who has two more children, will give birth to another child next month.
Gardaí were still at the scene of the incident on Wednesday evening as they tried to piece together what had happened.
Their investigation includes examination of the scene and a car by forensic collision
Ennis parish priest Father Tom Ryan visited the Ballaghboy stop on the city's Quin Road, where he offered his condolences to the boy's parents and members of their extended family.
On Wednesday evening, he met the child's bereaved parents and extended family and offered prayers.
Father Ryan had baptized the child, along with his siblings, and also married the children's parents.
Father Ryan said the boy would celebrate his second birthday in October.
“This is just a pure tragedy that has affected a family – a tragedy of the worst kind,” Father Ryan said.
“I visited the family this evening and we gathered for a small prayer service in the grounds of the site. I pray for each of them that they will have the strength they need at this time to deal with the devastating news that has befallen them today following the death of this little child in the tragic accident.”
Father Ryan added: “The condolences and prayers of the community are with them.”
He said the visit to the site to be with the family was “necessary”.
“It's not just any family, it's families, because they are all extended families that are immersed in grief and tragedy every second,” he said. “They need support and as a pastor I offered them that support and I would have known the family for years.
“I had the privilege of marrying my parents a few years ago. They are devastated and trying to come to terms with this news.”
Father Ryan said the boy had two sisters and their mother was expecting another child next month.
Gardaí said a family liaison had been appointed to support the family.
The boy's death brings the number of road deaths nationwide to 72 in 2024.
The number of deaths already exceeds that of last year. According to the Road Safety Authority (RSA), a total of 184 people died on Irish roads in 2023. Last year's total was a 19 percent increase in road deaths compared to 2022.