The government has said it cannot order the release of a critical report into how Cumbria Police investigated the death of Poppi Worthington.
The baby, from Barrow, was sexually assaulted by her father before her sudden death in 2012, a judge ruled.
Barrow MP John Woodcock has called for the Independent Police Complaints Commission report to be made public.
But Home Office Minister Karen Bradley said the IPCC believed the move could jeopardise a fresh inquest in March.
A draft copy of the report, leaked to the BBC, said the initial police investigation was "not conducted diligently and expediently".
It stated Cumbria's acting chief constable Michelle Skeer took more than a month to hold a meeting over the concerns raised in March 2014 by a High Court family judge who found no "real" investigation was conducted for nine months into the toddler's death.
In a Commons debate, Mr Woodcock said the Cumbria force's "astounding failures" highlighted in the report should be made public.
He also said Ms Skeer should not be allowed to continue in post because of her links to the investigation into Poppi's death.
But Ms Bradley said while the circumstances surrounding Poppi's death and the subsequent police investigation were "distressing and disturbing", she would not order the IPCC to release the full report.
She said the IPCC was holding its report back ahead of the second inquest, which opens on 18 March in Cockermouth, and a Crown Prosecution Service review of its previous decision not to pursue criminal charges.
She added senior police appointments were a matter for the Cumbria force and the county's police and crime commissioner.
However, she said police and crime commissioners could get the power to access IPCC reports which mention candidates for chief officer jobs, in the wake of the "troubling" Poppi Worthington case.