The Kangaroos will begin their 2021 World Cup defence against Fiji in Hull and could meet the Bati again in the semi-finals after the release of a draw that precludes an Australia-New Zealand final.
Australia have been drawn to play Fiji – semi-finalists at the last three World Cups – just hours after England kick off the tournament against Samoa before an anticipated 52,000 crowd at Newcastle's St James Park on October 23.
The world champions will also face Scotland at Coventry's Ricoh Stadium on October 29 and Italy at Wicked Stadium in St Helens, where Kangaroos coach Mal Meninga is fondly remembered from his playing days with the Super League club.
Assuming Australia finish top of Group B, they will then play the runner-up of Group C – comprising of New Zealand, Ireland, Lebanon and Jamaica – in Huddersfield.
If Fiji are second in Group B, they would play the winner of Group C – paving the way for a rematch of their 2017 quarter-final in Wellington, where the Bati upset the Kiwis.
The Kangaroos would then play the winner of New Zealand-Fiji at Elland Road, Leeds, for the right to meet the victor of the other semi-final at Arsenal's Emirates Stadium in the World Cup decider.
England is the top seed in Group A and Tonga is ranked No.1 in Group D, with a rematch of their epic 2017 World Cup semi-final clash in Auckland appearing likely.
The draw, which was announced on Tuesday, sees the Kangaroos also playing Scotland at Coventry's Ricoh Stadium on October 29 and Italy at Wicked Stadium in St Helens, where Kangaroos coach Mal Meninga is fondly remembered from his playing days with Saints.
The Jillaroos will face the Cook Islands on November 10, France on November 14 and the Kiwi Ferns on November 18, with all three pool matches at York's Community Stadium.
Both Australian teams won their finals at the 2017 World Cup in a double-header at Suncorp Stadium and will be hoping to repeat the feat at Old Trafford on November 27.
New Zealand, coached by Wests Tigers mentor Michael Maguire, play Lebanon at Warrington's Halliwell Jones Stadium on October 24 before back-to-back matches at Headingley Stadium in Leeds against Jamaica and Ireland.
Tonga, who stunned the Kiwis in 2017 and lost narrowly to England in the semi-final, have two games at St Helens, where their coach Kristian Woolf is now based, against Papua New Guinea on October 26 and Wales on November 1.
Their final pool match will be against the Cook Islands at Middlesbrough's Riverside Stadium on November 7.
After playing Samoa in Newcastle, England will face France at the University of Bolton Stadium on October 30 and Greece at Sheffield's Brammal Lane on November 6.
The Australian Wheelaroos play England on November 11, Norway on November 14 and Spain on November 17 at London's Copperbox Arena in the Wheelchair World Cup.
Full 2021 World Cup draw
Men's
Group A
Oct 23: England v Samoa at St James Park, Newcastle
Oct 25: France v Greece at Keepmoat Stadium, Doncaster
Oct 30: England v France at University of Bolton Stadium
Oct 31: Samoa v Greece at Keepmoat Stadium, Doncaster
Nov 6: England v Greece at Bramall Lane, Sheffield
Nov 7: Samoa v France at Halliwell Jones Stadium, Warrington
Group B
Oct 23: Australia v Fiji at KCOM Stadium, Hull
Oct 24: Scotland v Italy at Kingston Park, Newcastle
Oct 29: Australia v Scotland at Ricoh Arena, Coventry
Oct 30: Fiji v Italy at Kingston Park, Newcastle
Nov 6: Fiji v Scotland at Kingston Park, Newcastle
Nov 6: Australia v Italy at Totally Wicked Stadium, St Helens
Group C
Oct 24: Jamaica v Ireland at Emerald Headingley Stadium, Leeds
Oct 24: NZ v Lebanon at Halliwell Jones Stadium, Warrington
Oct 30: NZ v Jamaica at Emerald Headlingley Stadium, Leeds
Oct 31: Lebanon v Ireland at Leigh Sports Village
Nov 5: NZ v Ireland at Emerald Headlingley Stadium, Leeds
Nov 7: Lebanon v Jamaica at Leigh Sports Village
Group D
Oct 26: Tonga v PNG at Totally Wicked Stadium, St Helens
Oct 27: Wales v Cook Islands at Leigh Sports Village
Nov 1: Tonga v Wales at Totally Wicked Stadium, St Helens
Nov 2: PNG v Cook Islands at Halliwell Jones Stadium, Warrington
Nov 7: Tonga v Cook Islands at Riverside Stadium, Middlesbrough
Nov 8: PNG v Wales at Keepmoat Stadium, Doncaster
Nov 12: Quarter-Final 1 (Winner B v Runner-Up C) at John Smith's Stadium, Huddersfield
Nov 13: Quarter-Final 2 (Winner A/RU A v Runner-Up D/Winner D) at Anfield, Liverpool
Nov 13: Quarter-Final 3 (Winner C v RU B) at KCOM Stadium, Hull
Nov 14: Quarter-Final 4 (Winner A/RU A v RU D/Winner D) at University of Bolton Stadium
Nov 19: Semi-Final 1 (Winner QF1 v Winner QF 3) at Elland Road, Leeds
Nov 20: Semi-Final 2 Winner QF 2 v Winner QF 4) at Emirates Stadium, London
Nov 27: Final at Old Trafford, Manchester
Women's
Group A
Nov 9: England v Brazil at Emerald Headingley Stadium, Leeds
Nov 9: PNG v Canada at Emerald Headingley Staadium, Leeds
Nov 13: England v Canada at Anfield, Liverpool
Nov 13: PNG v Brazil at KCOM Stadium, Hull
Nov 17: Canada v Brazil at Emerald Headingley Stadium, Leeds
Nov 17: England v PNG at Emerald Headingley Stadium, Leeds
Group B
Nov 10: NZ v France at LNER Community Stadium, York
Nov 10: Australia v Cook Islands at LNER Community Stadium, York
Nov 14: NZ v Cook Islands at LNER Community Stadium, York
Nov 14: Australia v France at LNER Community Stadium, York
Nov 18: France v Cook Islands at LNER Community Stadium, York
Nov 18: Australia v NZ at LNER Community Stadium, York
Nov 22: Semi-Final 1 (Winner B v RU A) at LNER Community Stadium, York
Nov 22: Semi-Final 2 (Winner A v RU B) at LNER Community Stadium, York
Nov 27: Final at Old Trafford, Manchester
Wheelchair
Group A
Nov 11: Spain v Norway at Copper Box Arena, London
Nov 11: England v Australia at Copper Box Arena, London
Nov 14: England v Spain at Copper Box Arena, London
Nov 14: Australia v Norway at Copper Box Arena, London
Nov 17: Australia v Spain at Copper Box Arena, London
Nov 17: England v Norway at Copper Box Arena, London
Group B
Nov 12: France v Wales at English Institute of Sport, Sheffield
Nov 12: Scotland v USA at English Institute of Sport, Sheffield
Nov 15: France v Scotland at English Institute of Sport, Sheffield
Nov 15: Wales v USA at English Institute of Sport, Sheffield
Nov 18: France v USA at English Institute of Sport, Sheffield
Nov 18: Wales v Scotland at English Institute of Sport, Sheffield
Nov 21: Semi-Final 1 (Winner B v RU A) at English Institute of Sport, Sheffield
Nov 21: Semi-Final 2 (Winner A v RU B) at English Institute of Sport, Sheffield
Nov 26: Final at M&S Bank Arena, Liverpool