Health Service staff are being "let down by the Assembly impasse" as a pay award cannot be implemented until the Executive budget is confirmed.
The Health Minister said he has accepted the recommendations made by pay review bodies but is unable to move forward with them.
On Tuesday, an independent review body recommended that health service staff should be awarded a pay increase of £1,400 for 2022-23.
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There is a separate recommendation of a 4.5% increase for doctors and dentists.
The DUP has blocked the formation of a powersharing Executive as part of its protest against Brexit's Northern Ireland Protocol.
A planned multi-year budget which would have prioritised spending in health has not been progressed due to the collapse of the powersharing institutions.
Alliance Party health spokesperson, MLA Paula Bradshaw said that the political impasse at Stormont is letting down hard working health workers and that the DUP's "political stunt" is impacting hard-pressed individuals and families.
She said: "It is deeply regrettable that once again the hard working staff in our health service are being let down due to the political impasse at the Assembly. The low morale among our healthcare workers due to so much pressure is well-known and this delay will further exasperate things: it is long gone time that the DUP faced up to the huge impact their current political stunt is hurting hard-pressed individuals and their families.
"I hope that the Health Minister does, however, continue to explore every avenue possible to see if these pay increases can be introduced without delay."
Responding to the recommendations of pay awards by the NHS Pay Review Body and Review Body on Doctors' and Dentists'
Remuneration, Mr Swann said: "I have considered the recommendations made by both bodies and would be content to recommend acceptance of these awards.
"In relation to the Agenda for Change Pay Award, this would maintain the previous commitments made by the Executive to maintain pay parity with NHS pay in England.
"However unlike my colleagues in other parts of the United Kingdom, I am unable to announce the immediate implementation of these pay awards locally as Northern Ireland still does not have an agreed Executive budget for 2022/23.
"Equally I welcome and support the recent letter from the three devolved finance ministers asking the Chancellor to increase budgets to address pay and other pressures, including in the health service."
Earlier this week, Stormont Finance Minister Conor Murphy joined with his counterparts in Wales and Scotland to call on Chancellor Nadhim Zahawi to develop a "fair approach" to public sector pay and ask for an increase in devolved budgets to deal with emerging pressures, including in the health service.
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