"There have been a small number of complex cases reflecting issues such as stress, depression, anxiety and relationship discord with family," it said.
"Additionally the impact of the recession, job insecurity and loss of income by other family members is displayed by growing requests from staff for council to buy out leave provisions."
The council employs about 6500 full-time equivalent staff, but announced in its emergency budget in July it would cut 500 or more jobs this year to mitigate a Covid-19-related revenue hit of about $475 million.
In a statement, deputy chief executive Patricia Reade said 2020 has been an exceptional year for the council.
The pandemic response has had an impact on people's workloads, as has the emergency budget and its associated cutbacks, she said.
"It is important to note that as well as changes to the budget, we have seen the reduction in projects and work programmes, so it is not always simply a case of cutting jobs and redistributing work, but some work is also discontinued," she said.
"In general, structural change can be stressful for people and we make every effort to provide support to all of those affected and involved."
Reade said regular staff surveys, like the ones referred to in the report, are an important way of understanding how people are feeling and provide a guide for its ongoing staff wellbeing programme.
The Public Service Association (PSA) represents many of the council staff affected. National secretary Erin Polaczuk said it has been a tough year for the union's members and council cutbacks have only added to it.
"A global pandemic is inherently stressful and like most New Zealanders, Auckland Council staff had a very difficult year. It obviously adds to this stress when your employer's financial difficulties are headline news," Polaczuk said.
"PSA members went the extra mile as essential workers because they know their neighbours need strong community services, especially in such hard times. Our members helped the council minimise costs without undermining or cutting back services Aucklanders rely on."
Polaczuk said the union expects to discuss the importance of protecting staff wellbeing with the council.
The staff health, safety and wellbeing report will be considered by the council's Governing Body on Thursday.
It follows news last week that an Auckland Council employee has died in a suspected suicide amid allegations of harassment and bullying.
Jenny Gargiulo, a principal environment specialist, died on December 1 in Auckland's Blockhouse Bay, police said. The coroner is looking into her death, which a spokesman said was suspected to be self-inflicted.
