Wolverhampton Council and the Black Country and West Birmingham Clinical Commissioning Group have written to the 24,000 people in the city who are eligible for a vaccine but have not taken it up.
Within 48 hours, 3,000 calls had been made from people wanting to take up the invite.
But the council has said there are "isolated reports" of a small number of letters being sent to people who either are not eligible or who have already received it.
A spokesman for Wolverhampton Council said: "The City of Wolverhampton Council and the Black Country and West Birmingham Clinical Commissioning Group have written to approximately 24,000 people in Wolverhampton who are eligible for the life-saving Covid-19 vaccine but, for whatever reason, have not yet had it.
"At the time of sending the letter, these included people aged 50 and over, people with underlying health conditions, frontline health and social care workers and carers; over 45s are now also eligible for their jab.
"We have had a very positive response to the letter, receiving almost 3,000 calls within the first 48 hours from people who have subsequently decided to book their vaccine.
"While the letter was sent in good faith, we are looking into isolated reports that it has been received by people who either might not be eligible for the vaccine or have already received it.
"We continue to urge everyone in Wolverhampton to get both doses of the Covid-19 vaccine as soon as they are eligible to do so, in order to give themselves the best possible protection against coronavirus."
Dr Salma Reehana, Clinical Chair for the Black Country and West Birmingham Clinical Commissioning Group, said: “Numbers of vaccinated people increases daily. Therefore, the data used to call people for their vaccination changes rapidly, which can lead to some people being contacted more than once.
“I would encourage all people who are eligible to have their vaccine when they receive their invitation.”