He declared that the goal of offering the vaccine to 15 million in the four top priority groups by mid-February would be met.
Striking an upbeat note, he stressed that medics could also administer more than 600,000 jabs a day, the record so far.
While the limiting factor on the roll-out was supply, he emphasised that it was “good and stable” and he could see “week by week supply all the way through to end of March”.
He declined to set a target for doing the next five of the nine priority groups, which is people aged 50 and over and all individuals aged 16 years to 64 years with underlying health conditions which put them at higher risk of serious disease and mortality.
With ten million jabs already administered, though, he told BBC Breakfast: “We will set out our target (for vaccinating groups 5-9) after we have hit our February 15 target.
“But you can do the maths. We did 600,000 in a single day — the deployment infrastructure that we’ve built can do as much vaccines as we get supply, so the limiting factor will be vaccine supply.
“You can see that in the next ten or so days, we’ve got to do another almost touching five million and so if we keep that rate up we will very quickly go down the list of the top nine.”
Department of Health documents have previously outlined the aim to offer the first dose to 32 million people in the UK in the top nine groups by spring.
Britain is already a world-leader in vaccinating its population, far outstripping the pace in other European countries.
Mr Zahawi, though, stressed that there could still be “challenges” in producing vaccines which could impact on the UK roll-out, as has already happened on the Continent.
The Government has set the goal of vaccinating the four top priority groups by mid-February: people aged 70 and over, care home residents and staff, frontline health and social care workers, and individuals particularly vulnerable to the disease.
The vaccines are being delivered at more than 1,500 centres.
“My target is the mid-February,” Mr Zahawi told Times Radio.
“You have seen we reached 600,000 vaccinations in a single day.
“I think we can go even beyond that in terms of our deployment.
“Our limitation is the vaccine supply. It remains stable and good, I can see week by week supply all the way through to end of March which is good news but of course that is the limiting factor as to how fast we can go.”
However, he is coming under growing pressure from Tory MPs to consider getting pupils back to class more swiftly and then moving on to re-open the wider economy and society.