The message, also signed by six unions, asks the payment to apply to all workers in the industry and run until domestic and international borders open.
However, he clarified on Monday that there will definitely be a “next phase” of support, though the government will take its time in deciding its composition.
The union has also said members will travel to Canberra tomorrow ahead of a separate vote urging the scheme to be widened to excluded businesses.
The chairman of Mildura has become Australia’s first airport boss to call for the JobKeeper scheme to be extended after it emerged the initiative is $60 billion under budget.
Prime Minister Scott Morrison has promised the scheme will be reviewed at the end of June, and also hinted it could be extended to more vulnerable industries.