Sinn Fein's championing of rights is a "sham" as they are responsible for blocking change, the DUP has said.
Lagan Valley MP Sir Jeffrey Donaldson said republicans denied the right of the public to have their Assembly members vote on matters of importance to them.
The DUP has come under fire at various gay Pride events in Belfast this week over the use of a petition of concern to block legalisation of same-sex marriage when the Assembly was sitting.
Sir Jeffrey said: "It should probably come as little surprise to anyone that Sinn Fein take an 'ourselves alone' attitude to democracy.
"Whilst very keen to talk about their mandate, they completely disregard the mandate given to every other political party.
"Whilst talking about equality, for Sinn Féin republicans must always be more equal than others."
Sinn Féin has said it will enter any new talks to restore power-sharing institutions in good faith but they can only be successful if they deliver equality, rights and respect for all.
Sir Jeffrey said it was blocking votes from taking place on public sector pay increases, reform of our health service or on improvements to broadband provision.
He noted no party had sufficient Assembly members to trigger a petition of concern, adding: "Sinn Féin's championing of rights is a sham.
"They are only truly interested in their own narrow sectional interests and will hold Northern Ireland to ransom to advance those narrow interests alone.
"Their boycott of the Assembly and Executive means it is Sinn Fein blocking any potential of change rather than action taken by the DUP."
Sinn Féin MP Orfhlaith Begley said since collapse of the institutions the DUP has continued to deny rights to Irish speakers, women, victims and the LGBT community, rights which are enjoyed by citizens everywhere else in these islands.
"The DUP has been supported in this denial of rights by a Tory government in chaos," she said.
"In return the DUP has given the Tories a blank cheque for a disastrous Brexit against the wishes of the people of the north and backed continued savage Tory austerity cuts to our public services, cuts to health, cuts to education and to our economy.
"The DUP walked away from a deal with Sinn Féin in February this year to restore the Assembly and the Executive before collapsing the political talks."
