An identical bill will be introduced in the House of Commons on Wednesday.
A bill aiming to establish same-sex marriage in Northern Ireland was introduced in the House of Lords on Tuesday.
Conservative peer Lord Hayward put his Marriage (Same Sex Couples) (Northern Ireland) Bill before the House of Lords on Tuesday afternoon.
Northern Ireland-born Labour MP Conor McGinn will put his identically-titled bill before the House of Commons on Wednesday.
The bill has now passed its first parliamentary stage and in line with parliamentary procedure, the formal first reading of the private member's bill was brief and was not accompanied by a debate.
Peers will have a chance to voice their opinions on the proposed legislation on its second reading.
On Tuesday, a 30,000-strong petition organised by the LGBT campaign group Love Equality was placed before 10 Downing Street calling for the Government's support for legislation change in Northern Ireland.
The bill called for, same-sex marriage to be legalised, same-sex marriages solemnised outside Northern Ireland to be recognised, provisions in the law for the conversion of civil partnerships to marriages, a review of civil partnerships to make provisions for rights to pensions and social security contributions for same-sex married couples and civil partners and to make provision for gender change by married couples and civil partners.
Lord Hayward said: “It gives me great honour to launch the Westminster campaign for equal marriage rights in Northern Ireland in the House of Lords.
“I am pleased to introduce the Marriage (Same Sex Couples) (Northern Ireland) Bill in the Lords with the support of the Love Equality campaign from Northern Ireland.
“I am particularly delighted to launch the Bill in the presence of Ulsterman John Henry, whose powerful story moved me and so many others in recent weeks.”
John Henry - brother of Ulster and Ireland rugby star Chris Henry - told the Belfast Telegraph in February of his regret at the way his brother had found out he was gay.
Patrick Corrigan, Amnesty Northern Ireland programme director and a member of the Love Equality campaign, said: “We welcome this important intervention by Lord Hayward.
"Our preference has always been for the Northern Ireland Assembly to pass marriage equality legislation, in line with the overwhelming support which exists among the public here.
“However, without functioning devolution for the last 15 months, we now look to Westminster to legislate."
Northern Ireland remains the only part of the United Kingdom where marriage for same-sex couples is banned.
In 2015, a majority of MLAs in the Stormont Executive voted to support equal marriage but were blocked by the DUP's controversial use of the Petition of Concern.