"What this is doing is bringing into sharp focus the stark differences in the management of the pandemic in the UK and what's acceptable up there versus what's acceptable in Australia and New Zealand. There's still a bit more water to go under that bridge before we can absolutely say we're getting on the plane."
Peters said the NZRL wanted to have assurances for both on the ground in England and for players and staff returning to Australasia. He pointed to the NRL's management of the latest Covid-19 outbreak in Australia as an example of the kind of protocols he wanted to see in place.
For the next few weeks, all 16 NRL teams will be based in Queensland, with the NRL taking over hotels and forcing teams into their own bubbles, due to outbreaks in Greater Sydney and Victoria.
While communication between the sport's national governing bodies and event organisers has been strong and regular, Peters stressed the need for detailed plans so the NZRL could confidently put their people on a plane.
"We would want to see this sorted out by the end of July. The onus is now on RLWC21 and their people to provide us with the plans we believe are necessary to make this thing happen safely.
"We've been asking for it for many months now. It's not a new request, and it's time for them to deliver some detailed plans."
While the NZRL signed the participation agreement, making it clear their participation was conditional, fellow league heavyweights Australia have not signed, and the Sydney Morning Herald reports Australian Rugby League and the World Cup organisers are a long way from an agreement.
NRL clubs are concerned the tournament will take too much of a toll on athletes given the current lockdown requirements back home and the extended nature of the previous season.
New Zealand and Australia have combined to win the last nine World Cups, with the Kangaroos winning 11 of the 15 tournaments.
Earlier this week, Warriors head coach Nathan Brown voiced his concerns on the tournament going ahead.
"We're in isolation up here because there are 65 people a day in Sydney getting Covid; there's 30,000 a day getting it in England," Brown said.