The All Blacks would likely withdraw from a tours programme beyond 2019 if agreement on a new season was not reached, NZR ceo Steve Tew said this week.
WR needed to find a better way of organising the test year and delivering an equitable financial model.
NZR relied on test match ticket revenue and a system which gave them proceeds from just two home tests in a World Cup year was untenable.
In a normal year, mid-year tests cut into Super Rugby and did not deliver the money the All Blacks were able to generate for their northern hemisphere hosts later every year.
"We need a different season structure to the one we have now and we are not going to default to the current one if we can't find one," Tew warned. "We are going to force that issue.
"If people are not going to the table then we will negotiate individual matches for 2020, which wouldn't be all bad for a short period of time."
His SA counterpart Jurie Roux said South Africa were keen to see a different system in place once the tours agreement ended in four years.
"Everyone in the game knows that we have an issue around the season structure and the impact on player welfare and World Rugby is already exploring new options," he said.
"There's no silver bullet for this problem and it is something that has been exercising minds for a number of years. But there is widespread agreement that there is no appeal in continuing the current model beyond the current tours agreement."