With most adults and many older children now vaccinated, the Joint Committee on Vaccination and Immunisation has recommended the programme be rolled out to youngsters in the five to 11 age group.
Speaking about the benefits of vaccination, Prof Leitch told BBC Radio Scotland’s Good Morning Scotland programme: “We vaccinate babies every single day, we vaccinate toddlers every single day.
“Vaccination in the round, that technology has existed for well over a century and is probably the greatest medical invention after clean water and has saved more lives.
“We think in Scotland the Covid vaccination has saved nearly 30,000 lives, so it is safe, it is good for your kid to get it, but that doesn’t mean we are going to line everybody up and inject everybody without consent.
“It is important we have those conversations at the right time, when we have got the drug available and the parents are ready for it.”
While coronavirus can be a mild illness for many who catch it, Prof Leitch said there are still “rare” cases where it causes “severe disease in young people”.
Asked if it is his recommendation to parents to get their children vaccinated, he replied: “Yes it is, unless you have a contraindication or a reason not to do that, a medical reason in one of your children or something else going on.”
In those circumstances he urged parents to speak to vaccinators, saying: “If there is anything you want to talk about, they are trained, they can answer your questions. If they don’t know the specific answer to your kid’s challenge, if they have got a rare complication or something, then they will have somebody else in the clinic who will be able to help them with that.
“So yes, it is my strong recommendation you think very, very carefully about vaccinating your five to 11-year-olds.
“It is unusual, but we are still hearing of children getting quite sick with this disease.”
Children are given a paediatric version of the vaccine, so they get a smaller dose then adults, with Prof Leitch saying more stock of this is needed before the programme can be rolled out to all five to 11-year-olds.
He explained: “We’re going to think about logistics over the next week or two about how and where and when we should do this.
“We’ve got to get the paediatric formula of the drug, we’ve got some of that, we’re giving it already to vulnerable children, kids who have had transplants, kids who are on chemotherapy for example, those who are more at risk of the disease because of their underlying immunity.
“But we need more of that paediatric version of the vaccine.
“What we’re then going to do with the logistics and how we’re going to do that consent conversation and how we’re going to do this, whether we’re going to send appointments, whether we are going to ask people to phone in, all of that we’re going to work out in the next little while.”