But they also decided they will not give up their efforts to get funding for the overbridge.
Mayor Annette Main said the entire Wanganui East community wanted the bridge replaced and council would put it into its 2016-17 annual plan.
The deteriorating bridge is already subject to weight and speed restrictions. It was marked for closure but a groundswell of community opposition prompted the council to reconsider.
Senior roading engineer Rui Leitao told councillors unless the bridge was replaced, it would have to close to all but pedestrian and cycle users in 2018.
Closing the bridge would mean diverting motor traffic along an alternative route through Wanganui East, but upgrading those suburban streets would cost $200,000 and take traffic over a railway crossing.
Ms Main said the council needed to take its argument to a political level, rather than dealing with the agency.
Infrastructure manager Mark Hughes said the situation was not helped when the council was obliged to sign off on three-year, 10-year and 30-year asset management plans before NZTA made its funding decisions.
"It's totally out of kilter and needs to work in the same timeframe as we do," he said.
Councillor Sue Westwood said decisions made by the agency, after the council had met its Audit Office obligations, would continue to impact on council programmes.
NZTA acknowledged the potential impact that increasing forestry traffic was expected to have on Wanganui's back-country roads and would work with the council over the next three years to help manage those heavy loads.
Mr Hughes said one option could see some rural roads designated for forestry traffic, with no maintenance carried out on them for 10 years.
Ms Main said the frustration in funding lay in the process itself, with the community having no opportunity to have input into NZTA decisions.
"We need to have some input at a political level. I can see a chink here and we should push for that gap to open. It's the Government we need to be talking to," she said.
Councillor Hamish McDouall said the Wakefield St bridge was "the canary in the coalmine".
"This funding is the most important issue in front of us and decisions made can leave massive holes in our budgets," he said.