The letter was sent to councils that are due to undergo local government reorganisation in the next few years.
Oxfordshire’s current two-tier system, with districts and a county council, is set to be scrapped and replaced with one or more unitary authorities by April 2028.
The Secretary of State said the government would “listen to councils” who are concerned about their capacity to deliver elections, along with transitioning to a new structure.
West Oxfordshire District Council and Cherwell District Council are both run by the Liberal Democrats, whose party leader Ed Davey has described potential postponements as “cavalier”.
Andy Graham, leader of West Oxfordshire District Council, said: “Local government reorganisation will require an enormous amount of work, however, that is well in hand with our partnership authorities who are working closely with us.
“As such, there is no practical reason to postpone the election and so we will not be responding to the government invite and elections in West Oxfordshire will take place as scheduled in May.”
Responding to the BBC about the government’s letter, Labour-run Oxford City Council previously said it was “carefully considering” its response.
It pointed out that elections are due to be held in Oxford in 2027 for a “shadow council” ahead of reorganisation and said that polls cost about £250,000.
A meeting of Oxford City Council will be held on Wednesday to decide if the authority will request a postponement.
Oxfordshire’s other councils – South Oxfordshire District Council, Vale of White Horse District Council and Oxfordshire County Council – do not have elections scheduled for May.