In the reorganisation of local government, all district and county councils are being abolished with plans for new unitary authorities to come into existence from May 2028.
Michael Mitchell, Liberal Democrat group leader, spoke in favour of holding the election.
He said the government was offering the Labour Party in Exeter a “get-out-of-jail-free card” to avoid defeat in the elections which it should refuse.
Conservative group leader and member for St Loyes, Peter Holland, said it would be “morally and ethically wrong to cancel residents’ democratic rights”.
Diana Moore, Green Party leader, said people expected elections to take place and they were “not a privilege but a right”.
Reform member Alison Sheridan said Labour were “wiped out” in Exeter in the Devon County Council elections in 2025 and claimed Labour members were afraid of suffering the same fate in elections in May.
But postponing the elections in May “is not about denying democracy”, said Duncan Wood, a Labour cabinet member. “It is about ensuring when residents vote, they are voting for a council that will actually exist and will have the power to shape and deliver their services.”
Council leader Phil Bialyk said he had listened to the views of all councillors but wanted to request postponement to focus resources on the transition to new unitary authorities.
Members voted by 21 for, nine against and seven abstentions, to approve a recommendation to note the minister’s letter and make a response by 15 January.