Three people went on to develop bowel cancer, one of whom died. The ministry said it wasn't possible to say if being included in screening would have changed those outcomes.
Clark ordered an independent review of the national programme, and apologised unreservedly.
Information now released under the Official Information Act shows the day before that announcement Clark received a report from his ministry detailing how more New Zealanders had been missed.
"A second issue has arisen with the pilot due to addresses being locked in the BSP [bowel screening pilot information technology system] potentially affecting 2097 people, seven of whom have subsequently developed bowel cancer," the ministry reported.
"The NSU [national screening unit], working with Waitemata DHB, will follow the same approach as for the previous issue."
In releasing information to the Herald Clark's office said while the initial advice was 2097 people could have missed out, that was later revised to 333. None of that group has a current diagnosis of bowel cancer. The ministry has sent letters of apology, and invited them for screening.
Asked why the issue wasn't outlined when he announced the review, Clark said in a statement: "I am aware of the issue, and it further vindicates my decision to hold an independent inquiry."
Clinical director of the national screening unit, Dr Jane O'Hallahan, said the ministry took full responsibility for the oversights.
"The second problem arose when some addresses in the bowel screening register were locked so they couldn't be overwritten … mail continued to be sent to an old address."
The ministry also confirmed another issue around the risk of expired test kits.
More than 200 people who received a negative result were advised to complete another test, after they returned their completed kits at least 10 months after it was sent to them. Of that group, 151 did another test, and no cancers were found.
Bowel Cancer NZ spokeswoman Mary Bradley said questions needed to be asked about why the ministry hadn't been upfront with the public.
"You have to wonder what else they have not told us about … the review needs to be very thorough and transparent so that procedures are put in place to ensure this doesn't happen again with other DHBs."
Each year more than 3000 New Zealanders are diagnosed with bowel cancer and more than 1200 die from it. There can be no warning signs that cancer is developing, and early detection is critical.
Bradley said the country couldn't afford any more delays in the rollout, and it was deeply-concerning the last five DHBs wouldn't start screening until 2021.
Hutt Valley and Wairarapa health boards began screening in July last year, and Waitemata moved from its pilot to the national programme in January. Southern DHB joins this month.
Screening will be offered every two years to men and women aged 60 to 74. Once fully implemented it is expected to detect 500-700 cancers a year.
When the first pilot started in Waitemata DHB in 2011 it didn't have direct access to the National Health Index (NHI), and the subsequent problems have created tension between the DHB and ministry.
In November then Waitemata DHB chairman Lester Levy wrote to Clark to defend the health board.
Shortcomings with the register were first identified at the end of the pilot's initial cycle in late 2013, and between that date and 2017 the DHB highlighted the register limitations on multiple occasions, Levy stated.
The ministry has said there is a difference in interpretation between it and the DHB and the current review will provide clarity.
