Councillor Tania Kerr liked the idea but was concerned at the council's lack of knowledge of the extent of the issue.
"How do we set rules on who gets funds and who does not? This might be very oversubscribed or undersubscribed."
In the same vein, other councillors asked if the $100,000 proposed for the fund would be enough.
Hawke's Bay DHB's Dr Nick Jones was at the meeting and said it would be the council's decision alone to set criteria for fund eligibility.
"That would need to take into consideration whether it's based on the severity of the illness or other criteria such as a person's ability to function or GP costs.
"We need to be clear that the medical community can't assist with these decisions - we do not have the information on how great the issue is, we wish we were in a better position to advise."
Hastings Mayor Lawrence Yule said the council needed to accept that such considerations would not be a perfect science.
"It will be a mix of health, hardship and welfare - we also have to accept we do not have a determined period of time that people can apply from or until."
Deputy Mayor Sandra Hazlehurst said it was important that other organisations such as the Hawke's Bay Regional Council and government agencies contribute, so the fund could potentially be increased.
Mr Yule said informal talks had been held with the regional council who were awaiting the Hastings council decision on the matter, and added that council staff were talking to ACC every day to get the corporation's most up to date legal position.
In order to avoid more delays, however, he said the council needed to agree in principal to support the fund.
"If we don't get on with this we will be discussing it for another month, or six months. We need to put a line in the sand and commit to it."
After further discussion, all councillors present at the meeting apart from Simon Nixon agreed to establish the fund.
The chief executive was authorised to set the criteria for allocation, in conjunction with other appropriate agencies, and that information would be circulated for councillors' input.
In addition, the council would approach the regional council and other agencies to see if they would take part and assist with funding.