The UK Government has said same sex marriage in Northern Ireland could be introduced via Westminster.
Northern Ireland Secretary of State Karen Bradley said while it should be a matter for the Stormont Assembly, if the matter was to be raised at Westminster it is the Government's policy to allow a free vote on matters of conscience.
She was responding to a written question from Labour MP Conor McGinn, who asked if she would bring forward legislative proposals on equal marriage for same-sex couples in the region.
Ms Bradley said: "In accordance with the Belfast Agreement, this is a devolved matter which should be addressed in the NI Assembly; but the power of the Westminster Parliament to legislate remains unaffected.
"If this issue were to be raised in Westminster, the Government's policy is to allow a free vote on matters of conscience such as equal marriage."
Northern Ireland is the only part of the UK where same-sex marriage is not recognised in law.
Several attempts in the Stormont Assembly to introduce marriage equality failed.
The DUP used a petition of concern to veto the bills, arguing that such legislation did not command enough cross-community support.
Human rights organisations and LGBT equality campaigners have been calling for Westminster to legislate for marriage equality in the region.
In August 2017 the High Court in Belfast dismissed two cases challenging Northern Ireland's ban on same-sex marriage.
Delivering his judgement, a judge said it was for the Stormont Assembly, and not a judge, to decide social policy.
However, the region has been without a devolved administration for more than 13 months following the collapse of powersharing between the DUP and Sinn Fein.
The latest round of negotiations to restore the institutions failed last week after the DUP pulled the plug on the talks.
After the talks process broke down, shadow Northern Ireland secretary Owen Smith said it was up to London to introduce legislation in such areas as same-sex marriage.