National's campaign chair, Simeon Brown, attempted to deter attention from the Prime Minister before the party's Tuesday caucus meeting.
"Quite frankly, this is a sideshow which New Zealanders are not focused on," he told reporters.
Facing repeated questioning about the party's leadership, Brown emphasised a need for caucus discipline.
"Caucus members who wish to talk to media should consider whether they should quit the leaking or quit the party," he said.
"There is a need for caucus discipline, and for all caucus members to know that, ultimately, we are a team. We have a role to play, which is to support our leader, to deliver for New Zealanders."
He would not respond to repeated questions about whether he was involved the statement of support for Luxon released by chief whip Stuart Smith a few minutes earlier.
"I would suggest you put those questions to Stuart Smith," he said.
Smith did not immediately respond to a question, via text message, about whether he wrote his statement.