As of Wednesday, fewer than 20 people had appealed against having to pay higher premiums for MediShield Life due to their pre-existing conditions, said the Health Ministry in a statement.
Those who sent in appeals had conditions such as cancer and heart ailments, a ministry spokesman added.
"Appeals are considered carefully on a case-by-case basis, based on the specific circumstances and medical information submitted by each appellant," the spokesman said.
"Appeals that can be considered favourably are, generally, those for which there is good documentary evidence that the appellant has fully recovered from the condition."
MediShield Life, which replaces the existing MediShield, will officially start on Sunday.
The compulsory basic health insurance scheme covers all Singaporeans and permanent residents, or around four million people.
Of this group, 25,000 will need to pay 30 per cent higher premiums for the first 10 years because they have serious pre-existing illnesses.
Around 2,000 currently have health insurance, but with exclusions on these conditions. The rest have no insurance at all.
Singaporeans whose net premiums go up after MediShield Life starts will get transitional subsidies of 90 per cent in the first year, to help ease them into the scheme.
These go down to 70 per cent in the second year, and 40 and 20 per cent in the third and fourth years respectively.
Lower- and middle-income households will get permanent subsidies, while members of the Pioneer Generation will get additional special subsidies.
Singaporeans and permanent residents who have been notified that they have to pay higher MediShield Life premiums can appeal to the Central Provident Fund Board by writing to email@example.com.
The board will review the request before letting the person know if he has to provide his latest medical report for review.
He may also appeal to the board in the future after he has fully recovered from his condition.