The contract, starting in 2015, covered administrative support to 39,000 Global Positioning System, dentists, opticians and pharmacists, such as processing payments, ordering supplies and moving medical records.
NHS England wrote to Capita to ask it to consider halting the closure of local primary care support service offices in 2016, a report has revealed.
Although no actual harm was identified, the NAO said administrative issues including 87 women being notified incorrectly that they were no longer part of the cervical screening programme had occurred.
The Pharmaceutical Services Negotiating Committee (PSNC) - which submitted evidence to the NAO investigation after writing to NHS England in 2016 to raise its concerns about the "unacceptable" service provided by Capita - said it agreed with the NAO's findings.
NHS England spent £90m on these services in 2015 and aimed to reduce its costs by 35% from the first year of the contract.
As part of its seven-year £330m contract, Capita also organises GP and pharmacy payments and GP pensions, the moving of medical records - for example if someone changes GP practice - payments to opticians and providing NHS stationery, pre-printed forms, and needles and syringes for primary care.
The report claimed neither NHSE or Capita fully understood the level of service and performance standards needed to ensure patients were not put at risk of harm.
So far NHS England has deducted £5.3m from payments to Capita as penalties for poor performance but expects it may have to pay up to £3m in compensation to primary care providers.
Amyas Morse, the head of the NAO, said: "Neither NHS England nor Capita fully understood the complexity and variation of the services being outsourced".
The NAO recommends that NHS England should determine whether all current services within the contract are best delivered through that contract or should be taken in-house by NHS England.
"NHS England's decision to contract with Capita both to run existing services and also simultaneously to transform those services, was high risk", the report added.
He added that value for money was about more than just cost reduction.
Meg Hillier, Labour and Co-operative MP for Hackney South and Shoreditch, and chair of the Committee of Public Accounts, said that NHS England and Capita's service provision was "over ambitious [and] disruptive...and potentially put patients at risk of serious harm".
"It is deeply unsatisfactory that, two and a half years into the contract, NHS England and Capita have not yet reached the level of partnership working required to make a contract like this work effectively".
Ms Anderson emphasised that NHS England, Capita and patients can not "afford another fiasco on this scale".
A Capita spokeswomen told the BBC: "The report notes that several organisations and legacy issues all contributed to underperformance". It has been acknowledged that performance has improved and Capita will continue to work with all parties to address the remaining service issues.
Capita accepted accountability for not meeting high standards of service previously, the spokesperson emphasised.