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The Canterbury District Health Board estimates vaccinations will increase to 37,000 a week by the end of August.
A spokesman says a number of the clinics are now operating extended hours to support the increase.
People in Group 2 continue to be vaccinated as well as some people in Group 3.
Group 3 includes people aged 65 and over, people with some underlying health conditions, pregnant people, people with disabilities, older Māori and Pacific people, the people they live with and their carers.
"There are more than 170,000 people in Group 3 in Canterbury. Because of this, we're inviting people to book their vaccination appointments in stages."
People in Group 4 will be starting to receive notifications about being able to make a booking, from tomorrow.
The first age band is people aged 60 and over.
The CDHB has been under scrutiny after it was revealed it was well behind on the plan for group 3.
RNZ reported in May that injections for those people wouldn't be starting until July, two months behind the national plan.