"You can't have too many discoveries like this before people start saying, 'Yes, but what does this man really think?'"
Peters said National's deputy leader Paula Bennett would be first to go, because "that's what jackals do. They don't go for the big animal. They go for the smallest and weakest one. And then it will be Simon."
The NZ First leader, who is coming to the end of his time as Acting Prime Minister, said he wouldn't give an exact date for the leadership change, "but one of these days you'll look back and say, 'he was right'."
Bennett has responded on Twitter, saying Peters has "no idea" and she has "never felt stronger".
National this week produced its own cannabis bill on the same day as the health select committee reported its findings on a government bill.
National's legislation would allow medicinal cannabis products to be treated like any other medicines and be available from pharmacies. It would be available on the recommendation of a doctor or nurse practitioner who would authorise a photo ID card for medicinal cannabis.
The bill is much broader than the government bill before Parliament, which effectively limits the use of medicinal cannabis to terminal patients because it provides a statutory defence to the use of cannabis products only to the terminally ill.
Peters told Newshub Nation his party didn't believe the legislation was perfect, but it would be re-examined and tweaked before becoming law.
"I think in the current form it is safe, but maybe just too safe, where people who need the medical help are concerned. Maybe too prescriptive. But we don't want to go the other way, where it is just free and on the market."
Peters said National's cannabis legislation showed its leader was "somewhat confused".
"He's out there pushing this issue really hard … we have got huge geopolitical situation and uncertainty abroad, we have got all sorts of things happening to the economy. And all of a sudden he has discovered hashish, so to speak."
Peters was more generous when assessing his own time as Acting Prime Minister.
"I proved some of the cynics wrong. The sky didn't fall in."
Bennett told the Herald she was not remotely concerned about Peters' prediction the jackals would come for her or Bridges.
"I haven't listened to Winston Peters to date and so I shan't start now.
He also said they were coming after the smallest and weakest and it is true I am a bit smaller, but I've never been stronger.
The only reason he's talking about us is because he's worried about us."
She said she had bigger things to think about than Peters, such as the direction the country was going and policies.