Mr Lotu-Iiga told reporters outside the House this afternoon that he first heard about the term "dropping" this week.
He said there were many allegations and rumours around Mr Evans death last month, and accused Mr Davis of "making things up".
Mr Davis said Mr Lotu-Iiga was told about the practice of "dropping" at a select committee last month.
A transcript of the select committee on June 24 confirms that Mr Davis questioned the minister about the issue, though he did not name Evans.
Mr Lotu-Iiga said at the time Mr Davis was "getting hearsay-type representations".
Prime Minister John Key said he would be concerned if the practice of "dropping" was raised with the minister previously.
"Of course I'd be concerned if that had really happened. My understanding is that's not a term that people understand or know.
"That is a situation where people would potentially be very seriously injured if not fatally injured - that's a very serious matter.
"If allegations were made that it was happening and people were getting hurt as a result then yes of course that would be an issue."
Mr Key said he had "total confidence" in the Corrections Minister because Mr Lotu-Iiga had initiated a coronial inquiry into Evans' death.
Mr Lotu-Iiga said the chief inspectorate was also investigating the death.
"If when they gather the facts it needs to be referred to the police, then it will be referred to the police."
Asked why the case was not referred to the police in the first instance given the allegations about his injuries, he said it was up to the coroner to first determine the cause of death.
Mr Key said that if Mr Davis was claiming that someone was murdered in prison, then he needed to take that to the police.