The Wales Audit Office has criticised how staff handled criminal records checks for volunteers on the council's Kerbcraft programme.
At one point, poor record-keeping meant auditors were unable to determine if volunteers had been checked or not.
Monmouthshire council said a "comprehensive and robust" action plan was being implemented.
The report said auditors were "extremely concerned" about "inconsistent, partial and misleading information" provided by the council in response to their work.
"The council has failed to provide a thorough and coherent evidence-based response to our enquiries and we have received inconsistent information about the chronology of events from officers," auditors wrote.
There was no suggestion in the report, produced in February this year, of any wrongdoing by a volunteer.
Under Kerbcraft, which was introduced by the Welsh Government in 2002 and is run by all 22 Welsh councils, children are taken out of school by trained volunteers to learn skills for crossing roads safely.
Monmouthshire received Â£50,000 a year from Welsh ministers to run Kerbcraft, which had been delegated to a private/public joint venture until 2012 when it was transferred to the authority.
In June 2015, the scheme was suspended because of concerns over record-keeping.
That meant auditors were unable to confirm if volunteers had previously been subject to disclosure and barring service (DBS) checks - which have replaced criminal records bureau checks - or health and safety checks.
"As a result, we consider that children were placed at risk during that time," the report said.
"The council held no central record of information relating to volunteers and it appeared solely reliant on verbal assurances from the Kerbcraft co-ordinator that safe recruitment arrangements had been followed by staff operating the scheme."
Following a council review, Monmouthshire told auditors it had put stronger measures in place - but despite improvements after the scheme restarted in September 2015, auditors found further problems.
Staff were not requesting or looking at volunteers' DBS certificates and the council was not following up references for some volunteers.
The report found children were "being put at risk because of continuing weakness" in arrangements for their safeguarding on the scheme that the council had not addressed at the time the report was published.
Opposition councillor and Labour group leader Dimitri Batrouni said: "It is deeply disturbing that auditors were provided misleading information by the council.
"We are talking about our children's safety."
From August 2016 and in response to audit office concerns, the council stopped using volunteers on Kerbcraft.
A council spokesman said the authority had now adopted an action plan and new procedures had been approved, along with improved governance arrangements.
The new policy appears to permit volunteers but limit them to six at once to simplify the checking and recording of information.
The council is due to consider a revision to its safeguarding policy on Friday.

Owners of Mila, a Bedlington Terrier, found her cowering in a bush in their Halesowen back garden on Thursday evening.
Burglars beat the dog - leaving her with nerve damage - after breaking into the house, West Midlands Police said.
Homeowner Julie Green said she was "heartbroken" to find Mila wounded by burglars, who did not steal anything.
"Whoever is responsible is heartless," said Ms Green.
"She is the friendliest dog and would greet anyone. Even though she is poorly she has been trying to roll over and wag her tail."
Vets believe Mila has neurological nerve damage, preventing her from placing her front feet on the ground.
Ch Insp Phil Dolby said police are following several lines of inquiry.
He added: "This did not happen in the dead of night - there will be people around the Albrighton Road area who could have seen the offender or offenders responsible for the break-in."
More on this and other Black Country stories
The way a road safety scheme was run by Monmouthshire council put children at risk, a report has found.
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