The speech at National's "central and lower North Island" conference in Palmerston North today followed several poor polls for the coalition and a concert of economists cautioning against tax cuts in this month's Budget.
Speaking to party representatives, Luxon said the coalition had no intention of changing tack.
"It's only just the beginning. We are moving at pace and we will continue to do so, quarter by quarter, year by year, to get us out of where we are to a much better place."
Luxon told the audience New Zealanders had given the coalition "a pretty big mandate" to turn the country around.
"We're not here to manage the status quo. We do not care about the pundits and commentators and what people say out there."
Looking ahead to the May 30 Budget, Luxon said he was proud of what Finance Minister Nicola Willis had achieved.
"I look forward to New Zealand getting that tax relief thanks to National being in government."
Party members spoken to by RNZ seemed less sure about the commitment, with many pausing or offering only cautious support when asked whether now was the right time for tax cuts.
Questions of defence
Agriculture and Trade Minister Todd McClay and Infrastructure Minister Chris Bishop earlier addressed attendees on their respective portfolios.
In a question from the floor, Western Bay of Plenty Councillor Margaret Murray-Benge asked McClay for a guarantee that the government's defence policy did not "stuff up" New Zealand's trading ability.
Murray-Benge is also the partner of former National leader Don Brash, a prominent critic of the Aukus defence pact.
In response, McClay said the government would continue to voice its positions "respectfully" and in such a way that no other country would be surprised.
"Doesn't matter whether it's the US or the UK or Europe or India or China, we owe them the courtesy of talking to them directly," he said. "It is important we continue to have that independent voice but we should use it responsibly."
In an earlier regional conference this month, party president Sylvia Wood exposed a potential tension in the coalition dynamic when she reportedly told members National needed to lift its vote from 38 percent to the mid-40s.
Such a feat would almost certainly require National to eat into the support of its partners ACT and New Zealand First. Recent polling has put the party's support at or below the 38 percent mark.
The gathering comes less than two weeks out from the coalition's first Budget. Luxon last week told business leaders not to expect any surprises - "no bells, no whistles" - and reaffirmed his commitment to tax relief.
Labour's vision for 2040
The event comes a day after an address from Labour leader Chris Hipkins, in which he too set out his ambitions for the country and contrasted them with the coalition.
Hipkins criticised the "coalition of chaos" for its "shambolic" start to the term and accused it of lacking vision.
"Now is the time for creative thinking, for new ideas, and, yes, for a bold vision for the future."
Hipkins gave a hint of what Labour's under-review manifesto might end up looking like, as he painted a picture of New Zealand in 2040 under his party's governance.
He referenced "dramatically" cheaper childcare, nearly no petrol cars, and "mega landlords... paying their fair share of tax."
Detail though was deliberately thin on the ground.
"We need to stay open to new ideas - and that means not locking ourselves into rigid positions right now, but making sure that we're taking the time to hear other perspectives, to generate fresh ideas, and to carefully listen to New Zealanders about what they want from their future."
