WELLINGTON, May 9 (Reuters) - New Zealand's finance minister Nicola Willis said on Thursday that her government's first budget will deliver savings, set an operating allowance of less than NZ$3.5 million ($2.1 billion) and prioritise frontline services.

"Our budget will deliver durable savings from government departments, delivered through reductions in back office costs, less money for consultants, and decisions to stop go-nowhere policies and well-intended but ultimately lower-value programmes," said Willis at a speech in Lower Hutt ahead of the May 30 budget.

Ministry and departments across government have been asked to make between 6.5% and 7.5% savings ahead of the budget, which has resulted in significant job cuts.

Willis said in some cases agencies including the Ministry of Health, Ministry of Education and the country's defence force would see their savings redirected into their frontlines services.

Willis said the budget will bring personal income tax change and it will increase the take-home income of 83% of New Zealanders over the age of 15 and 94% of households.

"Our tax relief will be funded from within the operating allowance through a mixture of savings, reprioritisation, and additional revenue sources," she said. "Our decision to fund tax relief in the budget will not add to inflation." ($1 = 1.6661 New Zealand dollars)

(Reporting by Lucy Craymer; Editing by Daniel Wallis)