Philip Dunne says he understands the frustration people have had waiting for vaccinations to become available, but has been reassured thousands will receive their first vaccine dose in the coming days.
Last week, Mr Dunne asked Health Secretary Matt Hancock to prioritise vaccine deliveries to those areas of the country, such as south west Shropshire, which have yet to deploy vaccine for over 80s in the community.
The call was supported by all of the county's MPs in a letter to Mr Hancock to boost deliveries of the Oxford AstraZeneca vaccine, which, unlike the Pfizer vaccine, does not have to be kept extremely cold.
Residents have started to be offered appointments for jabs from Thursday at the Wellbeing Centre in Church Stretton for those who can travel, and through local GP practices for those who cannot.
Mr Dunne said: “I was very pleased to learn on Saturday the vaccination programme will get going on Thursday this week for local people over 80 who are living independently.
"People will be contacted by phone, email or letter by their GP practice to be offered an appointment with date, time and place.
"I am aware of the frustration many have had in south west Shropshire waiting for vaccinations to become available.
"I know in a few cases this stemmed from having vaccination appointments cancelled.
"I am also pleased that all care home residents and staff across south Shropshire have received their vaccinations.
"More than 4,000 over 80s registered at the nine practices within the south east Shropshire primary care network have also been vaccinated already at the Bridgnorth medical practice.
"Provided vaccine supplies arrive as planned, I am assured that the roughly 4,000 over 80s in south west Shropshire will be vaccinated by the end of this weekend.
"This will be a huge task for the GPs and their staff at the medical practices in Bishop’s Castle, Church Stretton, Clun, Craven Arms and at both practices in Ludlow.
"But will come as a great relief to those who have been waiting for their vaccines for the past few weeks."
He said the next significant task after that will be to vaccinate the next two cohorts of over 75s, over 70s and those younger people who are clinically extremely vulnerable, by mid-February.
"Deployment will be made easier by the planned opening of a vaccination hub at Ludlow Racecourse, expected next week," he added.
"I want to thank all the fantastic staff of our NHS in south Shropshire, who already face considerable pressure at this very busy time of the year.
"Many will be working long extra shifts, including over the coming weekend, to help keep the most vulnerable safe.
"I have been doing what I can to ensure we receive a fair and timely delivery of vaccine, calling in particular for the Oxford AstraZeneca vaccine to help south Shropshire catch up.”