At issue are two sections in a co-operation agreement signed between Ottawa and the territorial government last month for the surface clean-up of the mine site.
City councillors say it's not enough to merely "discuss" with the city remediation activities the two governments plan to undertake over the next 10 years or more it will take to clean up the site.
"We got a huge interest in that property," said Coun. Wendy Bisaro following a council committee meeting, Monday.
"If somebody else decides what the plan is going to be and then just tells us about it, then that may not fit in at all to where we want to go with it," she said.
The city acquired the lease for the old Giant Mine town site five years ago, with an aim to re-develop it for residential and recreational use. The site is on the shore of Yellowknife Bay where waterfront property is at a premium.
Bisaro said she is also troubled by a clause in the agreement that states one of either parties can back out of it after three years, should a remediation plan fail to materialize.
"I'm skeptical about how quickly governments can get things done," said Bisaro.
"Three years sounds like a long time but if somebody, somewhere in some department drags their heels, we could be up to three years in no time ... It could put us 10 years back easily."
The city is also at odds with the two governments over a policy to clean-up mine sites to industrial grade only.
The latest agreement states that any party who wishes to clean up Giant Mine, including the town site, beyond that threshold will have to pay for it.
No one knows how much it would cost to clean up the town site to a residential standard, which is considered contaminated with arsenic.
"What's the additional cost of bringing it residential standard?" asked Coun. Blake Lyons.
"I think that's a cost the public would be interested in."