The Constitutional Convention has recommended that the offence of blasphemy be removed from the constitution.
The 100-member group has voted to remove the clause and replace it with a more general provision against incitement to hatred on the grounds of religion.
The convention will now prepare a report for the government, which will have four months to respond with a plan on whether to hold a referendum.
The convention will now turn its attention to a range of other issues being suggested by members of the public.
The convention voted by 61% to 38% (with 1% undecided) to change the reference to blasphemy, with 53% voting for it to be replaced with a provision covering incitement to hatred on religious grounds.
Speaking about the work of the Convention, the chairperson, Tom Arnold, said was the convention "assess[ed] these issues in a respectful and dispassionate way."
"It was incredibly important that all sides of this discussion were treated in fairest possible manner and the arguments for-and-against were treated with the utmost respect," he said.