It comes after Health Secretary Humza Yousaf urged people to go for their booster jag ahead of Christmas.
In total, 72.1% of those eligible to get their Covid booster have been given the jag, with more than 70,000 boosters being given out in Scotland over the past two days.
Humza Yousaf said: “Getting vaccinated is your civic duty, you not only protect yourself, but your loved ones, those you interact with and the country as whole, so please get your booster as soon as you can.”
Speaking on the BBC’s Good Morning Scotland radio programme on Christmas Eve, Professor Leitch urged people to be “as careful and as cautious as they can be” as Omicron causes a rise in Covid cases with cases going up by over 50% in the last week.
Professor Leitch said: “Test before you meet other people and get yourself vaccinated.
“We are open all day today. There are lots of drop ins, lots of appointments available for today as not everybody wanted to come on Christmas Eve for the vaccine – they’d rather shop and see their families.
“So if you can squeeze in a vaccine and you haven’t had one or you are due your booster then please, please, please come today all over the country.”
On why vaccination sites are not open on Christmas Day, Professor Leitch said they did not expect a “big ask”, the vaccination programme is going well, and “the teams could do with a day off”.
The Scottish Government has urged people to get ‘boosted by the bells’, which it said was the best way to combat the Omicron coronavirus variant.
Professor Leitch also said the PCR testing system is “holding up, however, it is “reaching the top of its ability” as it is “very busy” .
“We do more PCR testing than pretty much any other country by population but we will keep increasing it,” Mr Leitch said.
This comes as the PCR test waiting time has been increased to 96 hours until tests come back after sending it away.