NHS chiefs made the plea after more than eight in 10 people aged 65 to 69 took up the offer of a jab across England.
Now they have called on people in the region to come forward as the vaccine roll-out continues to "gather pace".
Alison Tonge, regional director of commissioning at NHS England and NHS Improvement in the Midlands, said: "We are now inviting people aged 56 to 59 to get their jabs and I urge everyone eligible to come forward as soon as possible.
"The NHS vaccine programme is committed to protecting the country against coronavirus and it is testament to our incredible staff that we can now move on to the next age group.
"The vaccines are both safe and effective, so if anybody who is eligible but hasn’t been vaccinated yet, I’d urge them to go online or call 119 and get themselves booked in."
More than 1.8 million people in the West Midlands have had their first dose since the vaccine was first rolled out in December, with more than 18 million people vaccinated in England.
The NHS is vaccinating people in order of risk – which increases with age – and people aged between 50 and 55 are set to be invited to have their vaccine shortly, chiefs have said.
People can use the national booking service to reserve a slot at an NHS Vaccination Centre or one of the pharmacy-led services across the country.
Appointments are staggered to allow for social distancing and people are being asked not to turn up early to avoid creating queues. Everyone will receive a health status check and a pre-vaccination assessment before they have their jab.
The booking service can be accessed at http://www.nhs.uk/covid-vaccination. People who can't go online can call 119 free of charge.