Cwm Taf Morgannwg University Health Board has reported an increase in abuse towards staff amid the vaccine roll-out across Wales.
Vaccinations officially started in early December for frontline health and social care staff.
It comes as the health board said it is seeing "unprecedented demand" on its services, with 559 suspected, confirmed or recovering Covid patients in its hospitals as of Monday.
It also said the number of confirmed Covid patients in ITUs across its sites was at its highest since the first peak of the pandemic.
The Welsh Government confirmed that more than 25,000 people had received their first jab in Wales on December 24. Individuals who receive their first dose must have a second within 21 days.
The pace of the vaccine roll-out has been criticised by the Welsh Conservatives, who claimed that the lack of access to over 80s in care homes was an issue.
The health board said that staff had received abuse over the co-ordination of the roll-out.
In a tweet on their social media, the health board said that it "welcomed patience and support" whilst staff continued to work through enquiries.
"There has been an increase in abuse towards our switchboard operators and other staff as we wait for the COVID-19 vaccine to be fully rolled out," it said.
"We understand concerns but welcome your patience and support at this time. Programme details here. Thank you."
On the Cwm Taf Health Board website, it says that people over the age of 80 will start receiving vaccinations in early 2021.
"We will be starting our over 80 vaccinations in the New Year. This will probably be done from an immunisation centre due to the required storage and transport of the current vaccine that is available to us," the website said.
"If further vaccines become available in the New Year, GPs may also be able to help with immunisations. Our over 80s are a priority and they will be contacted and offered an appointment time for their vaccination."
A Welsh Government spokesperson said that people over the age of 80 were a top priority for the vaccine.
"Along with frontline health and social care staff, care home residents and staff, people over 80 are the top priority for the vaccine as set out in the schedule by the Joint Committee on Vaccination and Immunisation, which is being following by all four UK nations," a spokesperson said.
“We are hoping the second vaccine – the Oxford-AstraZeneca vaccine – will be approved by the UK regulator as this will help us accelerate our vaccination programme and provide more clinics in primary care settings, like GP practices.”