The National Party will reach out to the Greens and NZ First to advance areas of common interest, but Bill English insists he is not trying to cosy up to potential coalition partners for the 2020 election.

And English is also suggesting that working with National was a good way to put pressure on Labour, and ensuring Labour's success didn't come at the expense of the other governing parties.

The National Party has just wrapped up a two-day caucus retreat in Tauranga, where English again insisted that he and deputy leader Paula Bennett had the full support of the caucus.

Despite winning the largest share of the vote, National found itself short of a parliamentary majority and without any support partners after NZ First chose a coalition with Labour, with the Greens supporting on confidence and supply.

English said the caucus discussed the failure to win the election and National's lack of support partners, and how to move forward - including working with NZ First and the Greens.

"We'll work with parties with whom we have a common interest. We've already put up legislation - for instance, the Kermadec's bill - in which the Greens have a strong interest.

"There will be times when we have a common sense of purpose with NZ First. They've got some quite significant differences among them on the economy, on law and order, and we'll be helping those parties to achieve what they want and what we want."

But he insisted he wasn't reaching out for potential coalition arrangements in 2020.

"We're not trying to do deals just after an election when they've all done a deal with each other. That would be naive.

"We're simply setting off down the path where, in the interests of New Zealand, we can form sometimes a common sense of purpose with parties who are part of the Government."

He added that working together might be to the advantage of NZ First and the Greens.

"The Greens and NZ First will want to work with us as a way of putting pressure on the Government, occasionally. Not immediately, and not on a large scale, but every now and then that will happen.

"Their bigger problem is how to deal with the range of views within the Government, and how to ensure that Labour's success isn't at their expense."

Asked about instilling discipline following leaks to the media about leadership speculation, he said he didn't need to.

"This caucus understands that if they want to be competitive in 2020, then they need to show they can manage themselves. It doesn't need a whole lot of reinforcement from me for them to understand that."

He again repeated that leading the party into the 2020 election would depend on his performance.

This morning National MP Mark Mitchell downplayed speculation he would run for the leadership, saying he is "a bit of a romantic" and wanted English to take National into the 2020 election.

"I'm a bit of a romantic because I believe Bill deserves to get up. He's shown he's got the toughness and resilience and he believes so much in the country that he will do that.

"I'd love to see him go through and lead us in 2020."

Other MPs were also saying they believed the English/ Paula Bennett combo could see the party through to 2020, including Maggie Barry, Jonathan Coleman and Judith Collins.