County Hall has agreed to continue pursuing the Norwich Western Link, amid rising costs.
Inflated construction costs - and the need to realign the route due to bats - have pushed the cost of the 3.9-mile mile road up to £251m from the previous estimate of £198m.
The price hike would mean the road, stretching from the A1067 Fakenham Road to the A47 at Honingham, including a viaduct over the River Wensum, would cost about £64m per mile.
While Norfolk County Council insists there remains "an overwhelming case", opponents argue the environmental harm and economic cost are too high.
At a meeting on Monday, Martin Wilby, the council's cabinet member for highways, transport and infrastructure, told his colleagues the road will cut traffic congestion, rat-running and delays to journeys.
Alongside this, he argued it would help businesses and create new wildlife habitats.
The cabinet agreed to continue with the delivery of the NWL project and will ask central government to fund £213.4m of the cost.
Labour's Emma Corlett described the plan as a "road to ruin" and there were no guarantees the extra costs will be funded by central government.
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