People over the age of 80 have been promised they will be contacted about their Covid-19 jab within the next four weeks.
Matt Hancock said the NHS was on target to offer the jab to the most vulnerable by February 15.
The comments come after it was announced that the vaccines will now be offered to the over-70s as well as those on the shielding list.
But concerns have been raised that many over-80s have not yet been offered their jab.
The Health Secretary said that parts of the country have made “very significant progress” and have moved faster than others.
He said these areas should not stop their progress and should carry on vaccinating other groups.
But he told a Downing Street press briefing that over-80s as well as care home residents, their carers and frontline health and care workers remain the “priority”.
He said: “Some areas of the country have done even better.
“There are some parts where the vast majority of octogenarians have been vaccinated.
“And there are some places, for instance Slough, who have vaccinated all of their care home residents.
“And this means that in those areas where the vast majority of people in the top two priority groups have been vaccinated, from today we can start moving on to the over-70s and those under 70 who are clinically extremely vulnerable.
“We’re doing this because it’s the best way both to maximise the pace of the rollout, and to deliver according to the clinical prioritisation, all with the goal of saving as many lives as possible.
“I want to say to anybody who is aged over 80 but hasn’t yet had their jab, we will reach you.
“The NHS will contact you and you will have your invitation to be vaccinated within the next four weeks.”
With regards to the areas which have made swifter progress than others, Mr Hancock added: “We don’t want to stop the areas that have effectively done that job already. We want them to carry on.”
But the Health Secretary said that supply is the “limiting factor”.
He added: “In terms of the differences in rates of progress in different parts of the country, there’s all sorts of reasons: it does take time to set up each of the sites, each site has to be approved, all that does take a bit of time to set up.
“By February 15, everybody in the top four groups will be offered the vaccine.
“I would want to get to care homes and those over 80 sooner than that.”
Mr Hancock said the NHS was “on track” to meet the mid-February target.
The data shows that half of over-80s and half of care home residents have now received their first jab, he said.