The call follows two sections of parapet on a 135-year-old building in Rattray St falling on to its roof on Wednesday, causing the roof to collapse inwards into the second storey.
Yesterday, the Mr Cull said it made sense to look at the city's policies on building safety, but there were complicating factors.
Mr Cull agreed with Dunedin structural engineer Stephen MacKnight, who said there were fewer than 10 historic buildings in the central city which might be dangerous, and they were not hard to identify.
However, he queried who would pick up the financial cost of officially identifying the buildings and examining them to determine the level of danger they posed to the public.
"If council was prepared to check the stability of the buildings, who would pay for the inspection?"
If we did find a building was unstable, we could charge the owner. But if nothing is found, who pays?
"You could argue, if you have to pay for a warrant of fitness on a car, you could do the same for a building."
However, Mr Cull said that was not an argument he wanted to express an opinion on.
"Should we be concerned about the stability of heritage buildings? Yes we should.
"But it's a big step to say to the owner of a building, 'You must do x, y, and z to your building for reasons other than safety'.
"The owner could legitimately say, 'What is the community doing to pay for it, because it's a building which benefits the community?'."
Mr Cull said it was "not unlikely" the council would look at a change of policy on the matter in the coming months.
It was also possible a review or mass inspection of all unoccupied or disused buildings over a certain age could be carried out to check their structural integrity, he said.
However, he did not want to pre-empt any council actions.
"When heritage buildings fall down, like the one on Rattray St, it should prompt council to consider options, but it's not guaranteed to make them make any changes."
CPG New Zealand Ltd structural engineer Matt Williams said work on stabilising the building was progressing well but would stop over the weekend.
Staff would build structural steel supports at CPG which would later be transported to Rattray St to stabilise the facade of the building.
The removal of bricks from the facade would resume on Monday.
Rattray St would be reopened to one lane of traffic during the weekend.
