The former Brexit Secretary claimed the case notes showed that “sub-optimal care” was involved in the the cases of Baby O and Baby C.
He noted the doctors involved in this had been prosecution witnesses.
The MP also repeated doubts about the validity of evidence provided by expert witness Dr Dewi Evans.
Sir David claimed “erroneous” statistical evidence against Letby was even worse than the ultimately discredited data used against Cheshire solicitor Sally Clark, whose conviction for murdering her two sons was overturned in 2003.
Letby, from Hereford, is serving 15 whole-life orders after she was convicted at Manchester Crown Court of murdering seven infants and attempting to murder seven others, with two attempts on one of her victims, between June 2015 and June 2016 at the Countess of Chester Hospital.
Justice Minister Alex Davies-Jones said it was “an important principle of the rule of law that the Government does not interfere with judicial decisions”.
She added: “It is not appropriate for me or the government to comment on judicial processes nor the reliability of convictions or evidence.”
Ms Davies-Jones later told the Commons that Letby could apply to the Criminal Cases Review Commission if she believed she had been wrongly convicted.
Letby lost two bids last year to challenge her convictions at the Court of Appeal – in May last year for seven murders and seven attempted murders, and in October for the attempted murder of a baby girl which she was convicted of by a different jury at a retrial.
