Last week, ministers told council leaders they would consider postponing local polls until 2027 if they requested a delay.
The government said some authorities were concerned about their capacity to run them alongside local government reorganisation, as well as the cost to taxpayers of holding elections for councils that are due to be abolished.
In Norfolk, two councils are due to hold elections in 2026.
All 84 seats on the county council should be up for grabs, after this year’s vote was already postponed.
Its Conservative leader Kay Mason Billig has said she still wants voting to take place.
However, in Norwich – where 13 of 39 seats are due to be contested – Stonard and Norwich City Council have remained silent, despite several requests for comment from the BBC.
“If Labour are planning to cancel elections without any kind of discussion or process, it’s unacceptable,” said Lucy Galvin, leader of the council’s second largest group – the Greens.
She said she had repeatedly asked what Stonard’s position was but “I still haven’t had a response”.
“Having a proper, transparent democratic process where people have agreed elections and stick to them is core to trust,” she added.