"If anything, a bit of a burst of speculation like this has probably hardened up support."
He was not surprised that there was talk about the leadership in his own ranks, but was not concerned about a breakdown in discipline.
"These are ambitious people who want to change the way the world works and see politics as a way of doing that.
"So I wouldn't be at all surprised if there was some talk. But I have to say the conflation of that into some kind of threat to my leadership I think is ridiculous."
He said whether he led National into the 2020 election would depend on his performance.
"The leadership of an Opposition party is contingent on performance. So I commit to the performance that is going to maintain confidence in my leadership."
English said he had full confidence in both Bennett and Joyce after suggestions they should step aside.
English said he took responsibility for National's failure to get back into Government after NZ First opted for Labour, but National was holding up its support well and he took some credit for that transition.
"I've enjoyed more support in the caucus, and the party membership and our supporters than ever."
Those named as possible contenders for the role include Simon Bridges, Judith Collins, Jonathan Coleman, and Amy Adams. Adams said she was backing English.
Simon Bridges said English and Bennett had his full support "and I hope they lead us for a long time to come".
"I was very surprised by this mini-saga over the last 24 hours. I have no idea where it came from and I'm sure it will come to absolutely nothing given the caucus' strong backing of Bill and Paula Bennett."
Bennett said it was "a bit of media speculation" and was confident she had the confidence of her colleagues.
She would not be drawn on what might happen if English stepped down, saying it was hypothetical.
"I've always said I'm not seeking leadership and that's not really an ambition of mine, but you guys won't believe that till it really happens, eh?"
English's hold on the leadership will be bolstered by the latest Newshub Reid Research poll which showed National was holding steady near its election night result of 44.7 per cent despite Labour's surge in popularity – and that of Labour leader Jacinda Ardern.
While English's support as preferred Prime Minister had dropped to 25.7 per cent from the 30s and Ardern's had risen to 38 per cent, about 53 per cent of those polled said English was doing well in his new job.
In Parliament, Labour wasted no time having fun at National's expense.
Finance Minister Grant Robertson took aim at Bridges, noting a sign of his ambition was growing a beard over the summer. National's upcoming caucus meeting would be in Tauranga which Bridges no doubt saw as "home advantage".
Bridges laughed that off. "Yes I grew a beard over summer but when I saw that Andrew Little, James Shaw and Trevor Mallard had them I knew it had to go."
Bridges is due to host a barbecue at his Tauranga home when National MPs go to the city for a caucus meeting next week. Bridges said that was simple hospitality by the local MP.