Mr Durkan said a Bill of Rights was included in the Good Friday Agreement and must be delivered.
He was speaking after MLAs debated the report of the Ad Hoc Committee on a Bill of Rights, of which Mr Durkan is a member, in the Assembly on Monday.
Said the Foyle MLA: “John Hume said that ‘the basis of peace and stability, in any society, has to be the fullest respect for the human rights of all its people’.
“A Bill of Rights will include protections for everyone in the North and it’s disgraceful that the DUP are once again using their own narrow-mindedness as an excuse to block something that will benefit people here.
“A provision for a Bill of Rights was included in the Good Friday Agreement and nearly 25 years on its time we saw it delivered.
“The importance of safeguarding the rights of all the North’s citizens is more important than ever, particularly following Brexit with the loss of EU protections.
“A Bill of Rights will provide protections in a number of different ways.
“We need protections for socio-economic rights, to ensure that every part of the North is treated fairly in terms of investment, for the fight against the climate crisis and to enshrine the rights of minority groups.
“The consultation process carried out by the committee showed the clear demand for a Bill of Rights here.
“While nobody would argue it will solve all our problems, it will give us a solid foundation to build on going forward.
“A Bill of Rights is in everyone’s interest and myself and my SDLP colleagues will continue to push for one going forwards.
“The DUP needs to learn that a win for one does not mean a loss for another.”