Cllr Andy Blatchford made his plea after spending 12 hours in intensive care at the John Radcliffe Hospital, Oxford, following an operation.
He said he went to see his GP for a routine appointment when he was advised to have a free scan.
Cllr Blatchford, who represents College Town as a Conservative member of Bracknell Forest Council, said: “I am approaching 65 and I went in for a scan and was told that 3% of men have an aneurysm.”
The scan revealed that he did have an aneurysm, requiring an operation to treat it.
Cllr Blatchford said: “I spent 12 hours in intensive care and I was on the verge [of death].
“I spent a couple of days in hospital but later was back out doing things.
“I didn’t think I was going to survive, since they found it late.
An aneurysm is caused when an artery expands and becomes a “balloon” like structure. If left untreated, large aneurysms can burst and cause acute internal bleeding and death.
Cllr Blatchford revealed that both his father and brother died of the same illness, aged 61 and 58 respectively.
Cllr Blatchford said the death of his father had made him more aware of his mortality, adding “ever since I was 35 I have lived every day like it was my last”.
He called on elderly residents in particular to make sure they stay healthy by booking themselves an appointment for a scan.
He said: “Every man aged 65 and over should get a scan because it only takes five minutes and it can definitely save your life.”
For more information about aneurysms and to see if you could be at risk, visit www.nds.ox.ac.uk/research/oxaaa
Cllr Blatchford is now looking forward to a busy year of activities in his role as deputy mayor of the borough, which included starting the Samaritans Run at Wellington College last month.