The 101 referrals include direct reports from victims, according to the Police Service of Northern Ireland (PSNI).
Their investigation into the church was announced in November.
It followed a church admission of "serious and significant failings in the central safeguarding functions of the Presbyterian Church in Ireland from the period 2009 to 2022".
In a statement on Thursday, the Moderator of the PCI, Right Reverend Dr Richard Murray, said: "We are saddened to learn of the figures contained in today's statement by the PSNI, but welcome the clarity that is being brought with regards to their ongoing criminal investigation."
What have police said?
Det Ch Supt Zoë McKee gave more detail on Thursday about the 101 referrals.
She said: "These include direct reports from victims, referrals from safeguarding partners and other parties.
"This figure (101) changes on a daily basis and all information received is carefully assessed, in line with established investigative, safeguarding and evidential procedures.
"Our focus remains on providing the best possible service to those most affected by the safeguarding failures. We are committed to the investigation of criminality and the protection and safeguarding of those who are or have been victims of crime.
"We are working closely with valued partners and continue to appeal for anyone with information relating to safeguarding concerns that was either known by or reported to the PCI [Presbyterian Church in Ireland] to tell us what you know.
"It takes huge courage to report and we have specialist detectives dedicated to this enquiry."
What has the Presbyterian Church said?
In the statement on Thursday, Murray acknowledged the bravery of victims, survivors and those with concerns who came forward.
He also said the church "apologise again to those who have suffered or been harmed due to our inactions or inadequate responses".
"For these, we continue to deeply lament," he said.
Murray added that the church remains "committed to cooperating fully with the police and encouraged anyone who believes they may have relevant information, or who wishes to make a report, to do so".
Earlier this week, a senior church official wrote to congregations telling them to keep any relevant documents.
The church said that at the request of the PSNI an email had been sent requesting "that all congregations take immediate steps to preserve all church documentation and material relating to their safeguarding activities".
On Wednesday, around 400 Presbyterians from both sides of the Irish border held a special meeting of their general assembly in Belfast. It was the second since revelations about safeguarding failings emerged in November.
It emerged at the meeting that the person in line to take up the role as head of safeguarding at the church, Dermot Parsons, had resigned last month from his current job and would no longer be taking up the position.
At the meeting it was decided to split a key senior church post into two jobs. The combined role of general secretary and clerk of the general assembly are to be separated.
As well as the police investigation, the Charity Commission for Northern Ireland has launched an inquiry into the church.
The Rev Trevor Gribben was until recently the head of the church, known as moderator.
He stepped down at the end of November saying that although he had not been directly responsible for the delivery of safeguarding, some of the failings happened when he held senior positions within the church.
The next meeting of the church's general assembly will be a four-day gathering in Belfast in June.