The bridge spans the Catlins River 12km west of Owaka, and has been closed since November last year, when an inspection uncovered damage to its loadbearing structure.
The Clutha District Council at a meeting in February agreed to replace the bridge with a single-lane concrete structure, at a cost of $700,000 and requested 70% of the funding from the NZTA.
But the NZTA said the bridge was an uneconomic structure, and asked the Clutha District Council to provide more information on how the loss of the bridge affects the area.
Council manager district assets Jules Witt said if the NZTA agreed to replace the bridge, then it would give the council the full 70% ($490,000). But if it did not, then the council would have to revisit its decision.
"We would struggle to spend $700,000 on a bridge [fewer] than 50 vehicles a day are crossing," Mr Witt said.
Catlins ward councillor Kevin Thompson said local farmers with property on both sides of the river were having to move stock for many kilometres because the bridge was closed.
Forestry blocks would be ready for felling in the next five to seven years, and moving logging trucks up and down the Morris Saddle Rd would be inconvenient and dangerous unless it was upgraded, he said.
Chief executive officer Charles Hakkaart said the council was considering what would happen to land values if there were no bridge, where the landowners lived in relation to the land, and how the absence of a bridge would affect farming, tourism and logging activities.
The NZTA could give the Clutha District Council a lump sum to help pay for the replacement structure, but then make the council responsible for maintaining it in the future, which would add pressure to managing the roading network, he said.
The bridge, which was being supported by scaffolding, was continuing to deteriorate and the council was considering removing it because there was concern it could collapse and dam the river.
Mr Hakkaart said he hoped to decide next week whether to remove the structure.
The Tawanui bridge is the last remaining part of the second Balclutha bridge, built in 1914.
It was relocated to the Catlins River at Tawanui when a flood on the Clutha River washed away most of the middle section.