Earlier outspoken councillor Dave Hookway had said he was "extremely concerned" by a number of points raised in last month's High Court ruling, so he was calling for a public investigation.
Rintoul Group's price for four sections of Twin Coast Cycle Trail was more than $630,000 cheaper than its competitors, a large sum for a small local authority even when government funding for the trail was taken into account.
"The true reasons for excluding Rintoul Group tenders must be made clear, and accountability sought for such decisions," Mr Hookway said.
He said a growing number of ratepayers were approaching him with concerns about the quality of council decision-making, and it appeared the lessons of a Serious Fraud Office investigation in 2014 had not been learnt.
While the SFO found no intention to commit crime it did find evidence "that both council members and employees apparently failed to comply with internal systems and controls designed to ensure that proper processes were followed in the approval of council projects and the expenditure of public money".
In March 2016 five companies, including Rintoul Group, tendered to build four sections of the Twin Coast Cycle Trail.
Rintoul Group had previously built the Kawakawa-Taumarere section but an evaluation group alleged inconsistencies in information supplied about the project, that it had not been finished and went over budget.
The council then excluded the company from the tender process and invoiced it for more than $60,000 in deductions.
Justice Mathew Downs ruled in the High Court at Auckland in May that the council was wrong to exclude the company, with the two sides given until this week to decide on compensation.
They could not agree so the amount will be decided by the High Court. A date for the hearing has yet to be set.