The MSP for the Glasgow region has called for the time gap between Scots receiving their first and second dose of the vaccine to be halved.
It comes after the World Health Organisation (WHO) revealed that Scotland had six of Europe’s top 10 Covid hot spots last week.
Meanwhile the ONS infection survey figures suggest Scotland has the highest rate of positive cases in the United Kingdom.
Mr Sarwar said: “We need a plan now for dealing with this and the clear route out of this is speeding up the vaccination process.
“By cutting the waiting time between first and second doses we can get people protected faster and ensure our response to the pandemic is keeping pace with the crisis.”
A Spokesperson for Health Secretary Humza Yousaf said an eight-week gap between vaccine doses was “optimal”.
However, according to advice from the committee on Joint Vaccination and Immunisation (JCVI), reducing the time gap below eight weeks would compromise the effectiveness of the vaccine and how long that effect lasts”.
He added: “We are progressing to the final stages of our successful vaccine rollout as quickly as we can.
“This is limited by supply, we can only give Pfizer to younger age groups, in addition, constraints on supply affect the pool of those who had their first dose eight weeks previously.”