Liberal MP Warren Entsch has warned his Coalition colleagues to "butt out" of the debate about marriage equality after the party rejected the opportunity for a conscience vote on the issue and the Prime Minister, Tony Abbott, supported a plebiscite.

The member for the north Queensland seat of Leichhardt, a long-term advocate for gay rights within the conservative Coalition, said fellow party members should now refrain from campaigning either for or against same-sex marriage.

Liberal MP Warren Entsch says Coalition colleagues have forfeited a right to campaign on marriage equality. Credit:Alex Ellinghausen

"We have deferred the decision to the people. Now I am going to say to all of my colleagues: butt out," he said.

"They have basically forfeited that right by making the decision that has been made. They had the opportunity [to vote] and they said no."