SINN Féin's Michelle O'Neill has called again for "meaningful dialogue" to resurrect the political institutions.
The party's northern leader also said the British and Irish governments should "spell out how they will implement previous agreements" if devolution is not restored.
Ms O'Neill said she wants to lead Sinn Féin into an Executive "based on the principles of the Good Friday Agreement" but it remains unclear when talks to address a series of sticking points with the DUP - including calls for an Irish language act - will resume.
Tuesday will mark a year since Martin McGuinness resigned as deputy first minister, triggering the collapse of party's power-sharing government.
Secretary of State James Brokenshire has come under pressure to cut MLAs' salaries as the impasse continues.
DUP leader Arlene Foster also said this week he should move to appoint direct rule ministers if a short period of further talks does not succeed.
Ms O'Neill said yesterday: "Locally elected ministers are best placed to run local public services and fight back against the threats of Brexit and austerity.
"It is my firm belief that this can happen soon but only if the institutions represent genuine and equal partnership government for all our people.
"If the DUP continue to block social progress and rights and won't embrace meaningful power-sharing, then there is an onus on the two governments to spell out how they will implement previous agreements in accordance with the wishes of citizens of this island, north and south."
The DUP accused Ms O'Neill, who was the health minister in the previous Executive, of placing "party political demands as a higher priority than growing waiting lists".
Strangford MLA and former education minister Peter Weir said: "There has been no reform of the health service because Michelle O’Neill walked away from her desk and away from the route map to deliver that reform.
"Sinn Féin talk about 'no return to the status quo' but refuse to engage in talks with other parties. Their actions do not indicate a party seeking to find solutions, but rather putting forward excuses for their intransigence."
Alliance deputy leader Stephen Farry stressed the "importance of rediscovering the meaning" of the Good Friday Agreement as the 20th anniversary of its signing approaches.
He also criticised the British government for "only meaningfully engaging with one party around Brexit, despite the implications for all of Northern Ireland and the UK".
Meanwhile, the UUP's justice spokesman Doug Beattie urged Secretary of State James Brokenshire to "announce exactly when" a consultation process on legacy issues will start.
"This consultation does not require a deal between Sinn Féin and the DUP to begin this important step towards dealing with our past and neither should they be allowed to block it because of its uncomfortable content," he said.
