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The decision was taken following a crisis two-hour summit involving F1's hierarchy, its governing body, the FIA, and a number of the sport's team principals in Melbourne, the BBC and Sky Television Association have reported.
Motorsport.com quoted sources saying a majority of the teams were unhappy to continue and the governing FIA would accept the decision.
There has yet been no official confirmation from F1 or the sport's governing body the FIA.
F1's move follows the tide of the sporting world after a series of events were cancelled or delayed on Thursday in response to the deadly disease which has claimed more than 4,600 lives.
McLaren chiefs told governing body FIA of their decision to pull out late on Thursday night, barely 24 hours before practice was due to start in Melbourne.