Figures show that less than 1% of people deemed to be in the high-risk Group 7 for Covid-19 have received a vaccine so far.
The Health Service Executive said that vaccination of this group, estimated to be 300,000 people aged 16-59 years, will be completed by the end of May or early June.
People in Group 7 are at high risk of developing severe disease if they catch Covid-19 due to underlying conditions.
Latest figures show that by Sunday, 2,780 people in this group had been given a dose of vaccine, representing less than 1% of the group total.
People in this group are being vaccinated by hospitals or GPs.
The HSE also said it appeared likely that some people in Group 7 may have been categorised incorrectly in the computer system as being in Group 4 when they got their first dose.
Group 4, which is for those at more risk than Group 7, is showing in excess of 110% vaccination.
The HSE said that these category errors are being corrected at the second dose and that a HSE Data Quality Team is working to correctly code people on an ongoing basis.
When people return for their second dose, staff are being reminded on the system to correctly categorise people.
The HSE also said that its priority is to administer vaccines to those in Group 4, and that it has moved on to Group 7.
The plan is to administer up to 60,000 vaccines to very high-risk and high-risk groups this week.
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