The DUP blocked a public consultation on same-sex marriage for Northern Ireland, the Assembly has heard.
Finance Minister Mairtin O Muilleoir said he had asked the Executive but was refused.
The Sinn Fein Minister said he will now "hand the baton" for legislation on same-sex marriage over to MLAs, some of whom are planning Private Members' Bills.
He told MLAs his proposal "was voted down in the Executive, and, therefore, I cannot proceed, as Minister, with that Bill."
The DUP, which has blocked same-sex marriage motions in the Assembly, said it had "stood by its commitment to family values and marriage and will continue to do so".