Around 1,000 housebound older people still haven't been given their first COVID vaccine.
However, the Tánaiste has assured anyone waiting that they won't be forgotten.
The issue has been raised by a number of TDs, who've highlighted cases of people in their 80s and 90s that are still waiting.
Several such cases have also been highlighted in recent weeks on The Hard Shoulder.
In the Dáil today, Tánaiste Leo Varadkar said more support may need to be given to the National Ambulance Service, which is handling this element of the vaccination campaign.
He said: "There are about 1,000 people who are housebound who are still waiting to receive their vaccine.
"Generally older people will be receiving the AstraZeneca vaccine in most cases, because it's the easiest one to transport.
"That work is being done by the National Ambulance Service, and is taking a bit of time."
He said he understands people are frustrated and worried about not knowing their vaccination date.
However, he insisted: "They won't be forgotten - they will get their vaccine."
Minister of State for Older People Mary Butler, meanwhile, said it's a particuarly difficult issue in rural areas.
She noted it might take 30-40 minutes to get between houses, and then another 40 mins to do the vaccination and stay to monitor.
However, she said the HSE should get in touch with all older people that are housebound and yet to be vaccinated to ensure them it is on the way
Yesterday, the daughter of an 86-year-old woman who is still waiting on a vaccine told The Hard Shoulder said she was 'horrified, dumbfounded and disgusted' at Taoiseach Micheál Martin's response to her mother's position.
Anne Kelly is housebound and her case was raised on Wednesday in the Dáil by Sinn Féin's Darren O'Rourke.
In response, the Taoiseach said such issues are usually dealt with "by engaging with the local doctor, by engaging with the HSE".
He added: "There are ways of sorting this out fairly quickly".
However, Anne Kelly's daughter Adrienne O'Doherty told The Hard Shoulder she only contacted TDs as a last resort after being 'caught up in a loop' for a week trying to arrange an appointment.
Minister Darragh O'Brien has apologised to Ms O'Doherty for the situation, saying such delays and issues "shouldn't happen".
The HSE told Newstalk as of last Friday there were 934 housebound patients yet to receive their first dose of a vaccine.