Te Whatu Ora / Health New Zealand is accusing two unions of knowingly scheduling two strikes for the same time on Thursday.
Junior doctors will strike for two days and NZ Blood Service workers for four hours - and with lower level action all week.
The Resident Doctors' Association (RDA) union said this was the third recent strike action by its members after Te Whatu Ora failed to moving on its requests for fairer working hours and pay.
In a statement, Te Whatu Ora chief people officer Andrew Slater said the agency was "frustrated and disappointed" that more than 2500 doctors from the RDA were still striking.
"We are deeply concerned these two strikes were knowingly scheduled at the same time, which compounds the patient impact.
"Our teams have undertaken extensive contingency planning to ensure that, as a minimum, life preserving services can be provided. "
Some operations were being cancelled but emergency departments would remain open.
The strike by members of the RDA is due to run from 7am on Thursday until 8am Saturday, 1 June.
Te Whatu Ora had been working on facilitation with the union, but the strike action went against the Employment Relations Authority's recommendation, Slater said.
"We have put everything we could into facilitation. The Employment Relations Authority recommended the union remove the strike notice while we work through this.
"We have approached this facilitation constructively and are extremely disappointed that agreement has not been reached.
"We have asked the facilitator to make a recommendation to the parties, as we simply can't afford to meet the union's demands."
Te Whatu Ora is offering all resident medical officers a pay rise of between 3 percent and 29.3 percent, which would mean average salaries would rise to more $20,000 by next year.
However, RDA president James Anderson said the "last minute" facilitated bargaining had left key issues unresolved.
"The employer is trying to clawback the 'exam step', the $5000 salary increase in our contract awarded once a resident passes their first specialist examination," Dr Anderson said.
"The 'exam step' has been in employment contracts for resident doctors for over 50 years and recognises the thousand hours of unpaid study we are required to do to pass our specialist examinations."
"Removing the 'exam step' demonstrates a profound lack of understanding from Te Whatu Ora of the signal it sends to a burnt-out workforce, in the middle of a vacancy crisis."
Anderson also said the union was unhappy with the pay rates Te Whatu Ora was offering its members, and a "pay freeze" for registrars.
NZ Blood Service industrial action
APEX and Public Service Association union members of the NZ Blood Service (NZBS) are taking rolling industrial action from 29 May to 19 June.
It will include a full withdrawal of service on 31 May for four hours by PSA members and 24 hours by APEX members, followed by an all-day withdrawal of service on 4 June.
The service collects and processes blood products and other tissue from donors and makes sure they are safe for use.
NZ Blood Service's website states some donor appointments would need to be rescheduled or cancelled during the strike action.
Earlier, PSA said its members were getting paid less than their Te Whatu Ora counterparts doing the same job. Seven months of talks had not yet resulted in any pay offer from the employer, the union said.
The New Zealand Herald reported Blood Service chief executive Sam Cliffe acknowledged the lengthy process and patience shown by union members.
Cliffe said pay equity claims raised last year by APEX and the PSA were with Health NZ-Te Whatu Ora, not the Blood Service.
"We are committed to matching the agreed Te Whatu Ora pay rates and we're having ongoing discussions with the Ministry of Health as we seek to reach a satisfactory resolution, while operating in an environment of financial restraint."
In its statement on Wednesday, Health New Zealand said it was not party to the negotiations between the NZ Blood Service and the unions.
Te Whatu Ora said patients should attend any scheduled outpatient appointment or treatment unless they were told otherwise.
People with non-urgent treatment should contact their GP in the first instance. Anyone unsure about whether they need emergency department care should contact their GP or call Healthline (0800 611 116) for free advice.