He was speaking at National's AGM in Wellington this morning, where he, leader Judith Collins and party president Peter Goodfellow addressed hundreds of delegates following a disastrous election result.
Collins spoke about the opportunities that lie ahead for National and how it can take power in 2023.
Goodfellow, who is up for re-election as president today, however, attacked the media and Prime Minister Jacinda Ardern.
But the most applause of the morning came after Key took aim at National MPs who have been leaking to the media.
"Here is my very simple advice to those who like to leak to the media – if you can't quit your leaking, here's clue quit the party."
He said even if the leakers somehow think they are doing the party good, that attitude is wrong.
"Disunity is reported as disunity because that's exactly what it is."
He said voters "hugely punish" disunity.
"The public look at it and say 'for goodness sake, if they can't run their own party, how on earth will they run a party."
He told MPs it was okay to disagree and to debate ideas - but that should be done privately.
"We shouldn't do it by going behind people's backs."
Meanwhile, Key also warned National Party faithful not to underestimate Ardern.
"Some people are going to tell you that eventually the public is going to get sick of Jacinda Ardern". But he said that was a mistake.
"It is exactly what the Labour Party said about me for nearly a decade. If we underestimate Jacinda and her advisers, we will be in opposition for a very long time."
Goodfellow's term as a board member has come to an end but he, along with South Island board member Rachel Bird, are both seeking re-election at the annual general meeting in Wellington.
Goodfellow has been party president since 2009.
Three board positions are up for grabs and four people, including Goodfellow and Bird, are in contention.
Outgoing long-serving MP and former Speaker David Carter is also putting his hat in the ring, along with former board member Grant McCallum.
There are nine members of the board - seven are elected and the other two are the leader and a caucus representative, who is usually a whip.
Elected members serve a term of two years, with four of the positions coming up in one year and the other three the year after.
This year there are three positions being voted on by the delegates, which includes MPs, and the constitution dictates that at all times one of the members must be from the Auckland/Northern region, and another from the South Island.
Currently Bird is the South Island representative so if she fails to be re-elected then Carter would be, on the basis he is the only other contender from the south.
The third vacancy on the board this year has come about after Roger Bridge tendered his resignation.
He was accused of attempting to derail a candidate for the Auckland Central seat with a late-night call to talkback radio.
- NZ Herald and RNZ
