The change means owners of some land and buildings targeted for compulsory acquisition by the council under the Public Works Act for the project have been spared.
The council has been working on a plan for five years to redevelop the Steamer Basin with apartments, bars and tree-lined boulevards.
Two weeks of hearings about possible changes to the district plan for the planned project will begin on Monday.
There had been concern from businesses that they might be forced from the area by higher rents, or by residents who did not want to live alongside industrial operations, if the project went ahead.
Businesses affected by the notices of requirement have said they could be forced to move from the area.
The council has withdrawn three of six notices of requirement, meaning a public square in Fish St, another in Tewsley St, and a walkway from Mason St to the harbourside will no longer proceed.
Council chief executive Jim Harland said one reason for the withdrawal was financial.
If the notices of requirement went through, and all the landowners called for the council to buy straight away, there would not be enough money set aside in the long-term council community plan.
Mr Harland said when valuers looked at the properties, it was realised the money set aside - there is $10 million for various aspects of the project in the plan - was not enough.
The project was originally sold as a 50-year vision, with areas closer to the water to be developed first, and areas such as the Tewsley St square longer-term projects.
Mr Harland said other areas might be identified in future for public amenities, and properties bought if they came up for sale.
Planning staff had changed and there was no longer support for the withdrawn squares and walkway, but there was strong support for the remaining amenity spaces.
Steven Thornton, managing director of Lindsay Walkinshaw Ltd, an importing and wholesale business at 14 Tewsley St, said he was relieved he would not lose his building.
He was not anti-development but "from a business point of view, it's one of those things you don't need".
He received a letter from the council earlier this week.
Valuers had visited the building, and a large percentage, the most profitable part, would have had to been bought.
Mr Thornton said he would not be surprised if the council had looked at the price and decided against going ahead.
"We're not the only ones in that situation."
A report to the hearings committee from council planner Deborah Hogan said a strong focus of submissions on the plan change was the ability of industry to continue in the area, and the harbourside's heritage value.
Submissions on the notices of requirement were "generally opposed" for similar reasons, she said.
