Yesterday, 44 road closures remained in place around the city and four dangerous building notices were in effect.
In announcing the relaunched fund, Mr Cull said individuals could claim up to $5000.
''We recognise that there will be a need for that and we are more than happy to make that available,'' he said.
Those wanting more details or to make an application could do so via the council's website.
Henley's residents, some of the worst-hit, were allowed to return to their properties yesterday and access to the settlement was reopened.
Watch Dunedin Mayor Dave Cull announce relaunch of mayoral relief fund:
It was unclear how many residents remained evacuated around the city, but it was only a ''handful'', Dunedin City Council recovery manager Simon Pickford said.
More than 40 people self evacuated, of whom only three remained out of their homes, and four residences were unoccupied due to buildings being unsafe, for which notices were issued.
''It's actually pretty minimal in terms of people out of their home at the moment,'' Mr Pickford said.
Mr Cull said anyone with concerns about the safety of their home should contact the council.
''Residents are free to return to their homes as long as it is safe to do so,'' he said.
Council staff and geotechnical consultants continued to assess the slips which littered the city's roading network and work was being prioritised based on need.
A decision on which sports grounds would be opened for the weekend would be made today, acting parks operations manager Gareth Jones said.
All grounds remained closed yesterday as a final assessment was being completed.
- Otago Daily Times