The right wing National leader has told Australia’s Prime Minister he can’t hold a free vote on equal marriage as it breaks the Coalition agreement.

The possibility of a free vote surfaced after Labor decided it would oppose legislation to hold a plebiscite.

Premier Malcolm Turnbull, who is in favour of introducing marriage equality, refused to rule out the possibility of a free vote in parliament.

However, Barnaby Joyce, head of the National party who form the governing Coalition with the Liberals, said to allow such a vote would breach their agreement and added that the Government can’t do it.

“All I will say on that is if all of a sudden the policy becomes a free vote, my firm view, and it’s not just a view it’s actually the reality, [is] that is breaking one of the tenets of the Liberal National Coalition deal,” he told reporters on Wednesday.

“That would be quite a serious matter so I don’t think that’s going to eventuate.”

A spokeswoman for the Prime Minister said that he was urging the Senate to pass the plebiscite bill, but wouldn’t say if changing policy to hold a free vote violated the Coalition agreement.

Earlier this week, Joyce ruled out the possibility of a free vote and said it would be “chaotic” for his party to revisit its position.

“The position is this: if you wish to change the Marriage Act, then support the plebiscite,” he added.

Joyce also denied he was in a spat with the Prime Minister over the issue and said “plan B” was to deal with other issues if the bill didn’t pass.

A recent survey revealed the majority of Australians are annoyed at how long parliament is taking to introduce marriage equality.