The NZ Herald reported on Monday night that MPs were again nervously questioning Mr Luxon's position, three months out from the November 7 election.
The reporting led Mr Luxon to call a snap meeting in Wellington on Tuesday morning in an attempt to resolve the question.
"Division and disunity are a major distraction only 90 days out from the election," he said on social media.
"This distraction is unfair to the New Zealand people, and dedicated National Party candidates, supporters and volunteers, when there is so much at stake."
Mr Luxon has led a three-party coalition of the National, NZ First and ACT parties since 2023.
Most polls show the right-leaning bloc would be returned to power at the forthcoming election, but National faces a drastic loss of its support, from 38 per cent at the last election to roughly 29 per cent.
The prospect of a reduced partyroom and diminished presence around the cabinet table - as well as the nuclear outcome of being the first National-led government turfed after one term - has prompted the tough conversations on Mr Luxon's future.
"There is no doubt that the destabilisation campaign within National has whirred right back into action," Radio NZ deputy political editor Craig McCulloch said.
Any MPs considering a coup so close to the election will be guided by the example of Jacinda Ardern, who took the Labour leadership seven weeks from the 2017 election, when she took office.
However, there are yet to be any declared challengers to Mr Luxon from a field which could include his deputy, Finance Minister Nicola Willis, Education Minister Erica Stanford, and demoted Transport Minister Chris Bishop.
Mr Luxon, who entered politics in 2020, has never quite shaken the background noise of leadership grumbles during his tenure.
That's partially due to his three-party coalition, the first in New Zealand's history, which includes veteran disruptor and maverick Winston Peters, the NZ First leader.
The pair need to work together in government but also campaign against each other, and are increasingly at odds as the election nears.
Mr Peters, 81, was chided as "racist" by Mr Luxon this month after heckling a Chinese-born Greens MP in parliament by telling him to "go back to where you've come from".
However, he was not reprimanded or sacked as it may have brought down the government, making Mr Luxon liable to the charge that he tolerates racism.
Mr Luxon, the former Air New Zealand chief executive, has also caused plenty of his own political problems.
This month alone, he apologised to small business operators after saying they had a "parent-child relationship" with government, and justified the use of defence planes ferrying him home from a party fundraising dinner.
He also made a captain's call to campaign for a referendum on NZ's electoral system, which drew pushback from his party and others both on the policy and how he did it: live on radio.
In April, National MPs resolved to keep Mr Luxon in his role after a marathon partyroom meeting considered the matter.
In the same month, Mr Luxon shook up his ministers and election team, stripping key moderate Mr Bishop of the campaign chair role in favour of conservative MP Simeon Brown.
Mr Bishop fronted media on Tuesday prior to Mr Luxon's meeting declaration, saying he hadn't talked to colleagues about a leadership change.
"We back our leader," he said.
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