"Coming from the South Island, having grown up in Christchurch, we are going to have representation absolutely.
"We've got to be representing all of New Zealand. We've got some great MP's in the South Island, advocating incredibly strongly. There is a bigger job to do in Christchurch and Canterbury in general," he said.
Luxon said he has been so busy since becoming leader, he has yet to speak with his parents.
"It was pretty busy yesterday and today. We've got to go to work."
He said it is well known the party's performance has been suboptimal.
"The bottom line is we're back and we have to earn the trust back of the people that have supported us."
Luxon said there is a lot of "crazy things" going on at the moment.
"The traffic light system, orange is very much about pressure on the health care system, yet the South Island's in orange, it doesn't make any sense."
Luxon succeeded in his bid to become leader yesterday, beating former leader Simon Bridges, who withdrew from the contest.
Bridges confirmed the move on Twitter and said he'd met Luxon on Tuesday morning and had a "great discussion".
"I am withdrawing from the leadership contest and will be backing Chris. He will make a brilliant National leader and Prime Minister," Bridges said.