Members of the adult social care and health scrutiny committee have asked for a report to be brought to their October meeting in order to allow enough time for it to be prepared.
The independent review of maternity services at the Shrewsbury and Telford Hospital NHS Trust found 201 babies and nine mothers could have survived if the NHS trust had provided better care.
Coun Maxine Callow, chairman of Blackpool Council's scrutiny leadership board, called for a report into local services saying she felt it was vital "to put our minds at rest" about the quality of the town's maternity unit.
Speaking after the meeting of the scrutiny committee, she said: "I am not saying there is anything wrong with Blackpool maternity unit, it's probably very good.
"But as a scrutiny committe we haven't looked at maternity services, and in view of what has happened at Shrewsbury and Telford I think it is something we should look at.
"We want to make sure in Blackpool we have everything right, and that will then be reassuring for anyone having a baby or planning to have one.
"I'm sure everything will be alright, but I just want to make sure."
An update on maternity services given to the board at Blackpool Teaching Hospitals NHS Trust in May 2021 said the needs of families was being put at the centre of all care.
Nicola Parry, head of midwifery at Blackpool Victoria Hospital, told a meeting of the board that listening to women and families was a vital part of providing a good service.
This has also included removing barriers to ensure women understand their choices when it comes to the delivery of their babies. Other measures include having “a robust pathway for complex pregnancies.”
Risk assessments are carried out throughout pregnancies and all midwives go through detail training programmes.
The Ockenden Review, led by senior midwife Donna Ockenden, considered the care of 1,486 families between 2000 and 2019, and has resulted in a number of recommendations for the NHS.