A request for a supplied photo was also declined as council "did not have a suitable photo".
This has raised concern with some who spoke out about the features' removal.
When asked, Napier RSA president John Purcell said they were worried about what state the features were in, and felt the public should be assured by council that the items were in a safe condition.
Neither he nor other RSA members had seen the items since they were removed, "all we know is its being kept in a council yard somewhere."
Historic Places Aotearoa Hawke's Bay branch chairwoman Barbara Arnott was doubtful the flame was being kept alight, but was "absolutely sure that memorial will be looked after".
"I think it will be lit in the future," the former Napier Mayor said. "I think if we trust that that will happen, that's enough for me, and it would be enough for [Historic Places Aotearoa]."
President of the Napier and District Grey Power Association - which recently condemned the removal - Laurie Jenkin said he would be concerned if the flame was not being kept alight, as then "it probably doesn't matter where it is while it's waiting for its new home".
Mr Jenkin - who had relations killed in the World Wars - said the flame was a reminder of those who had to "pay the price", and wanted the features reinstated.
Napier resident Alan Rhodes -a spokesperson for the "Save the War Memorial" group - said he felt carting the features around had done a disservice to the memory of those killed in the World Wars.
"The secrecy doesn't make any sense to me, because these [features] were made to be seen, not stowed away somewhere."
His attempt to visit the features had been refused. He said he was interested due to the amount of publicity about the flame being kept alight, when it had been unlit for periods previously.
In response to the concern, Council CE Wayne Jack assured both items were being looked after at the Onekawa Depot.
He agreed when asked if he felt people's concerns were unfounded.
"The flame was offered to the RSA's and they didn't want to hold it, so the flame is being held at a council facility and it is continually lit."
Napier mayor Bill Dalton could not be reached for comment.
Public sentiment has been that the memorial features should return, if not to the centre, to Marine Parade - one of the new locations being considered by the council's War Memorial Project Group.
Recently they had discussed over 12 potential sites for the war memorial, council's Manager Visitor Experiences Sally Jackson said - with the RSA's indicating a preference for a Marine Parade site.