Hamilton City Council's debt is forecast to be $609 million by 30 June 2021.
Council's Finance Committee Chair Rob Pascoe applauded the LGFA for moving quickly to potentially provide councils with more "breathing room" but urged caution.
"This has the potential to give councils more options and that's a positive move because nearly all councils will be under immense financial pressure including ours. But this shouldn't be seen as opening the floodgates to a deep well of new money that eventually ratepayers down the line will have to pay back," he said.
"We need to exercise caution and, in my personal view, make sure that any additional borrowing we might incur would be for essential spending only.
"We need to be prudent because more debt means more financial risk to the city and its ratepayers."
Mr Pascoe said to partner with government on big economic stimulus packages, councils would be expected to have "skin in the game" and contribute financially.
"For us, it would still be a stretch to fund some of those projects, even with greater debt capacity. It's a balancing act."
And while borrowing rules might be loosened temporarily, he expected they would be pulled back when the economy recovers.
"So there's no free pass here. Any extra money would have to be repaid."
Council chief Executive Richard Briggs said if the council increased its debt to help the city recover from Covid-19, any spending would need to be carefully targeted.
"Debt is very useful in that it can pay for large infrastructure used across multiple generations. It means the burden of paying for that infrastructure is also spread across generations, which is fair," he said.
"Councillor Pascoe is right to be cautious. But it's good to see this change being considered, along with changes to the Resource Management Act. These are the sort of measures councils will need so we can play our part in kick-starting local economies."
Hamilton Mayor Paula Southgate endorsed Mr Pascoe's comments but noted council had not formally discussed the issue.
