Simon Bridges says if National formed a coalition with New Zealand First, he wouldn't let Winston Peters have a "presidential veto on everything".
Appearing on The AM Show on Monday morning, Mr Bridges refused to answer questions on whether he trusted Mr Peters, saying it wasn't "a question of trust", but competence.
"It's an issue of competence and who's got, I suppose, the positioning over the other. Jacinda Ardern knows New Zealanders are coming to the conclusion that she's not running the show. He has the presidential veto on everything. I wouldn't let that happen, I can give you that assurance."
Former National leader and longtime Prime Minister Sir John Key famously ruled out working with Mr Peters in 2011, going as far to say if NZ First held the balance of power on election night there would be a Labour-led Government.
Mr Bridges refused to say if he'd rule out working with Mr Peters.
"I need some things to talk about come election time. We'll make our position quite clear then. Do I trust him? I haven't had close dealings with him like that... but it's not actually an issue of trust."
National remains the highest-polling party, as it was on election night, but lacks viable coalition partners. Mr Peters began his career with National, and sided with them after the country's first MMP election in 1996 - but since then has formed Governments with Labour under Helen Clark and Ms Ardern.
Mr Bridges said the result has been a "tragedy" for the country.
Last week, polling firm Ipsos said "the current Labour-led government is perceived to be doing a better job at present than the National Government was" a year ago, by a score of 5.4 out of 10 to National's 4.9.