The union representing 27,000 public sector nurses said that did not go far enough, and it wanted an improved offer from the district health boards next week.
The independent panel was set up last month to break the impasse between nurses and their employers, at Ms Ardern's suggestion.
It yesterday recommended the slightly higher pay increase than the 2% offer which was rejected last month, plus a $2000 lump-sum payment.
NZ Nurses Organisation (NZNO) industrial services manager Cee Payne said the recommendations on pay fell short of addressing the union's concerns.
Members would want to see a ``significantly improved'' offer from DHBs which addressed core issues of staffing, pay and working conditions, she said.
Ms Payne said the panel's recommendations concerning staffing were positive.
It recommended DHBs receive additional funding to ensure they had the capacity in the nursing workforce to deliver services.
The last pay offer by DHBs in April was 2% over two years and a lump sum of $1050. If the NZNO does not accept the offer next week, a winter strike is likely.
The NZNO has said it would prefer to settle with DHBs than to strike. But it said its members were dealing with an ageing and increasingly sick population, and staff were stretched because of a decade of underfunding of the health system.
In a rare move, the union began a month-long secret ballot of its members on strike action on April 23.
Any pay increase will likely require more funding from the Government. Last week's Budget included contingency funding for health sector pay rises.
There was also $100 million over four years to increase community midwives' pay.
The independent panel comprises former Whanganui District Health Board chief executive Julie Patterson, former Reserve Bank director Professor Margaret Wilson and former NZNO chief executive Geoff Annals.
