Dr Sandesh Gulhane, the Scottish Conservatives' health spokesman and a practising GP, said it is "crucial" every step is taken to get jags into arms.
It follows reports NHS Lothian, Scotland's second-largest health board, previously warned it was "not possible" to significantly ramp up its vaccine capacity.
A total of 71 cases of the Omicron variant have now been identified in Scotland.
The Tories have repeatedly called for mass vaccination centres to reopen to help meet the target of every adult being offered a booster by the end of January.
Dr Gulhane said: “It is crucial that the SNP ensure every step is being taken to get jags into arms as quickly as possible.
"Re-opening mass vaccination centres which were successful in the initial rollout would be a major help, but the SNP have so far failed to heed repeated calls from the Scottish Conservatives on this front.
“If they won’t open up larger sites, they must ensure there is sufficient capacity where jags are being delivered."
Dr Gulhane accused SNP health secretary Humza Yousaf of "passing the buck to health boards to sort his mess out", adding: "We saw during the first rollout that there was an army of volunteers willing to come forward to get jags into people’s arms.
“We are not seeing any solution from Humza Yousaf to sort out staffing and capacity levels to ensure every adult is offered a booster dose by the end of next month.
“We need to see communication and leadership from the SNP over this latest stage of the vaccine programme.”
The Daily Telegraph reported that NHS Lothian last month refused a request by the Scottish Government to offer boosters to all over-50s by Christmas, citing staffing and capacity issues. The health board told the paper it was now "gearing up" to deliver boosters "as quickly as possible".
On Sunday, Mr Yousaf said NHS Greater Glasgow and Clyde had trained 100 additional vaccinators last week and will train an extra 100 this week.
He said: "We're increasing capacity. We're going to health care students, we're going to independent contractors, dentists, optometrists and whoever else, to try to increase that capacity."
Mr Yousaf said Scotland was leading the rest of the UK "by some distance".
He said the Scottish Government was looking to increase the number of vaccine clinics, and would not "discount" opening mass centres.
Elsewhere, Deputy First Minister John Swinney encouraged Scots to take lateral flow tests more than twice a week, as he said he takes a test every time he leaves home.
He said the Government wants people to take the “very reliable” tests more frequently.
Proof of a negative test now enables entry into venues subject to the vaccine passport scheme.
Mr Swinney told the BBC’s Good Morning Scotland radio programme there was now a “high level of vaccination in society”, meaning there could be more flexibility around the rules for entry into places like nightclubs.
He said: “We want people to increase the frequency of the use of lateral flow tests, away from the two times per week to much more frequently when they are socialising and interacting with others.
“Personally I am now doing a lateral flow test every day I am going out with the prospect of meeting other members of the public outside my household.”
A Scottish Government spokesman said: “Scotland already has the highest vaccination rate of all UK nations for first, second and third doses. The winter vaccination programme has already delivered more than 1.8 million booster and third doses to the most vulnerable groups. This is more than 40 per cent of the adult population.
“We aim to offer a booster to everyone aged 18 or older who is eligible by the end of January, in line with the JCVI’s advice, and we’ll explore all options to accelerate the vaccination programme as quickly as we possibly can.”