He also told MLAs “everything was on the table” when asked if he would consider reintroducing mass walk-in vaccination centres to speed up the programme.
The Assembly was debating changes agreed by the Executive to Covid regulations in Northern Ireland, including removing the need for social distancing in theatres and cinemas.
During the debate, TUV leader Jim Allister said Northern Ireland was “dragging far behind” the rest of the UK in the rollout of the booster vaccine.
He said: “The figure that has been quoted is 28%, less than half of some other devolved regions.”
Mr Swann responded: “In regards to the booster programme, can I say I am slightly disappointed in where we are.
“I have engaged with our CMO (chief medical officer) and our vaccination team to see exactly where we are.
“While we have been able to support our GPs, one of the things that didn’t keep up was actually putting the data on to our vaccine management system.
“We have now asked PHA (the Public Health Agency) to look at how they can actually enhance that administration system.”
Asked if he would consider the return of walk-in vaccine centres to speed up the booster programme, Mr Swann said: “When we met yesterday everything was on the table.
“We are looking at where we can go. I want to see where community pharmacies and GPs can actually start to deliver.”
The booster vaccine is available for the over-50s, to be administered no earlier than six months after their second jab.
SDLP and Alliance MLAs criticised the absence of a mandatory Covid certification system for entry into hospitality settings.
On Monday, the Department of Health announced it had launched a new domestic verification app which can be used by hospitality venues.
However, it is on a voluntary basis as the Executive has not agreed on a mandatory system.
SDLP MLA Justin McNulty said: “We are hearing about the challenges being faced by our emergency departments and the threat of closure of some of those emergency departments.
“Everyone in this house should recognise the need for vaccine certification while we are in this situation. To me it is a no-brainer.
“Anything that can encourage more people to get vaccinated, to lessen the demands on our health service, to shorten the waiting lists, it is a no-brainer. Why is there opposition to it?
“Vaccine certifications are a proven alternative that will allow us to prevent another lockdown. Who could be against that?”
Alliance MLA Paula Bradshaw said the situation around face coverings is “now bordering on farce”.
The Executive recently agreed that face coverings could be removed when dancing in nightclubs but must be worn in other indoor settings, excluding when eating and drinking.
Ms Bradshaw said: “It is now common to see people, including staff, in shops and elsewhere simply not wearing face coverings.
“The non-wearing of face coverings indoors is permitted in some instances.
“Ultimately we have to make a decision. If we are keeping face coverings in regulations, we need to enforce those regulations. Alternatively, we need to accept that we are now solely on guidance as so many people are not wearing them at all.”
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