National's campaign director, Steven Joyce, said his party would "obviously talk with New Zealand First over the course of the coming weeks" but a deal was unlikely.
Mr Peters said there would be only one reason National would want a deal - "that would be to get us off their back". He added: "The election is over. They've won for the time being and we know what our job is and we're going to do it ... keep them honest, to ensure that they're transparent."
Having criticised Labour for its infighting and the Greens for "attacking" Labour during the campaign by questioning its fiscal plan and suggesting they might talk with National, Mr Peters was positioning NZ First as the leading Opposition party.
But four-term parliamentary veteran Mr Mark, who was courted by National before he chose to run again for his old party, said NZ First was looking to advance its policies.
"If it means playing a completely opposition role, then so be it, and if it means playing a support role in some areas, our caucus will have to meet and have a conversation about where to from here, but I'm not pre-empting or prejudging anything until I've had a chance to sit down with the boss."
The development of a constructive relationship with Mr Peters and NZ First could make sense for National in terms of ensuring potential allies after the 2017 election.
"It would make sense that they're looking forward to that," said MP Richard Prosser. "But until we get back to Wellington and sit around the caucus table and have a yarn about what's been suggested and where we might like to go I couldn't give you a steer about that."
Mr Mark, who will give up his job as Carterton's mayor and has been touted as a potential successor to Mr Peters, said he did not necessarily believe those ahead of him on the party list would be his seniors in the new-look 11-strong NZ First caucus.
"We've got new caucus members who are totally new to Parliament and some who are only just starting their second term. In my eyes they are still learning."