Wes Streeting has branded calls to free Lucy Letby “crass and insensitive”.
The Health Secretary said that the public should continue to view the former nurse, who is currently serving 15 life sentences, as a murderer amid growing demands for her release.
Letby was convicted of killing seven newborns and attempting to murder seven others at the Countess of Chester Hospital between 2015 and 2016.
But there is growing pressure to free the 35-year-old, with some doctors, scientists and statisticians questioning the way that evidence was presented to the jury.
Asked about the row by LBC’s Lewis Goodall, Mr Streeting said: “It is crass and insensitive to be waging a public campaign in this way. Because we can debate it, you and I, listeners can debate it, we can read the newspapers.
“We’re not the Criminal Case Review Board. We have an independent judiciary in this country, I think we have a fair and successful independent judiciary in this country.”
The Health Secretary’s intervention is the first public comment on growing doubts about the safety of Letby’s convictions by a member of Sir Keir Starmer’s Cabinet.
It comes as the family of one of the babies who died told those raising concerns about Letby’s conviction, “shame on you”, adding it has made them question humanity.
Appealing to the public to let the judicial process “run its course”, Mr Streeting added: “There is no purpose to a media campaign.
“It is for the courts to decide on the basis of evidence and I would just remind people that we always presume innocence until people have been found guilty.
“Lucy Letby has been found guilty, on multiple counts, of serious crimes with multiple whole life sentences.
“And until the courts find a reason to suggest otherwise, we should continue to regard her as a convicted killer serving multiple life sentences, delivering justice for those families going through unimaginable and intolerable grief.”
The Thirlwall Inquiry, which was set up to examine how Letby was able to harm babies in her care while working at Countess of Chester Hospital, is due to begin on Tuesday.
The probe will also examine the broader conditions in the neonatal unit where Letby worked.
David Davis, a veteran Tory MP, last month revealed he hoped to visit Letby in prison as part of an investigation as to whether she may be the victim of a miscarriage of justice.
Mr Davis told The Daily T podcast he would hope to visit Letby in HMP Bronzefield in Surrey if he was “at least three-quarters persuaded that she’s innocent”.
Experts from universities including Edinburgh, Harvard and Bristol have joined members of the Royal Statistical Society in questioning the way crucial evidence was presented in court.
Doubts have also been raised over Letby poisoning liquid nutrition bags fed to the victims with insulin, as there was no direct evidence that the bags had been tampered with.
But the parents of twin boys Baby E and Baby F, one of whom was murdered and one of whom was attacked by the nurse, have said calls to free Letby have been fuelled by “lies and misinformation”.
“Our family is deeply shocked by the ongoing speculation surrounding what is being referred to as a miscarriage of justice,” they told the Sunday Times.
The parents added: “Once they were all put together the wall of evidence was overwhelming. To take each brick out separately is simply taking evidence out of context.
“The spread of lies and misinformation is deeply distressing and makes us sick to our cores. We just want some peace to grieve, knowing the person who caused so much agony is where she belongs.”
Last year, Letby failed to face her victims’ families when she was given a whole life order for murdering seven babies and trying to kill six more.
It led Sir Keir, the then opposition leader, to call on Rishi Sunak to introduce a new law to make offenders appear in court.
Mr Justice Goss, the judge in the trial of Letby, told the court he did not have the power to force her to attend her sentencing, saying there was “nothing I can do about it”.
On Tuesday, a public inquiry will begin into Letby’s crimes at the Countess of Chester Hospital.
It will hear evidence from senior managers at the hospital, medical staff and lawyers representing the victims’ families. It will not look at questions over her innocence.
But the calls for the case to be re-examined have gathered momentum since the verdicts were handed down last August, with particular concern expressed about some of the scientific evidence presented to the jury.
One of the key planks of the prosecution case centred around a spreadsheet showing the frequency of child collapses against Letby’s shift patterns.
But leading statisticians have questioned the legitimacy of such evidence pointing to miscarriages of justice in the Netherlands and Italy involving medics accused of killing patients in their care.
In 2010, Dutch nurse Lucia de Berk, who had been convicted of seven murders, partly based on shift pattern evidence, was cleared.
And three years ago Italian nurse Daniela Poggiali, who was accused of murdering up to 38 patients was cleared of wrongdoing.