Mr de la Poer asked if she was “deliberately” trying to “withhold” information about someone possibly harming babies.
Ms Kelly replied: “No, as I have said, on reflection there were actions that I didn’t get right but the actions I did take were done with good intentions.”
The inquiry heard Ms Kelly’s safeguarding referral came in March 2018, almost a year after Cheshire Police were first called to investigate unexplained deaths and collapses on the unit.
Ms Kelly accepted the referral was “not detailed enough”.
Mr de la Poer asked: “Is it because you had a feeling of hostility towards the consultants and you didn’t think the police investigation was going anywhere?”
Ms Kelly said: “That’s not true.”
Before questioning began, Ms Kelly asked to make a statement to the inquiry in which she expressed her condolences to all of the families affected.
“I’m really sorry for all the distress they’ve experienced over the last few years and are currently experiencing as we sit here today,” she said.
“I didn’t get everything right at the time, however the decisions I made were done with the best intentions.”
Letby, then 34, was convicted of murdering seven babies and attempting to murder seven others, including two attempts on one infant, between June 2015 and June 2016.
She is serving 15 whole life sentences.
The public inquiry is now in its 11th week and is expected to sit until early 2025.
Its findings will likely be published in autumn next year.