"Given the appalling nature of child abuse we need to look very carefully to make sure that what was done in the past did indeed cover everything that it needed to do and was done properly," May told the BBC's "Today" program.
The action follows several ongoing investigations into widespread allegations of abuse by former BBC personality Jimmy Savile.
Savile, who died last year at the age of 84, has been accused of abusing as many as 300 people in a 40-year period. There was no indication he had anything to do with the Wales children's home but the names of the 28 alleged abusers were never made public.
Reopening the Wales inquiry comes after an abuse victim charged the original investigation did not fully examine claims.
The three-year investigation heard from 650 people who had been cared for at the Bryn Estyn children's home.