The party has been refusing to take part in the Stormont Assembly until issues they have raised over the post-Brexit trading arrangements are addressed by the UK.
DUP MLA Edwin Poots has insisted his party will “stay strong”, claiming the current government has inflicted more damage on the union than anything else in the 100 year history of Northern Ireland.
However Sinn Fein MLA Conor Murphy has said patience is running out with the DUP, urging them to end their boycott of Stormont.
“The reality is the Windsor Framework was agreed months ago. The DUP are still staying out.
“They were given reasonable space to get their party in the place where they would stop the boycott of the Assembly, undo the continuing damage that Tory rule is doing to the people of the north and patience has run out with all of that.
“That deal is done between Europe and the British government. The DUP have got all of the space that was reasonably required for anyone to process this, take it through their party and take a decision to get back into government with the rest of it, as they were elected to do, to respect the outcome of the last election, another day’s delay is a delay too long.
“They need to get back to work with the rest of us.”
Earlier Mr Poots told the BBC that he encouraged DUP leader Sir Jeffrey Donaldson “to be strong at this point” in a recent meeting.
“The damage that this Conservative government has done to the union has been greater than anything that has happened over the course of the last 100 years of Northern Ireland’s existence, and therefore the response that they need to invoke is a response which is one of significance and one which actually helps secure the union for years to come,” he said.
“This Conservative government has been woeful in how it has treated the union and how it has treated the people of Northern Ireland.”
Mr Poots also insisted that the DUP is not giving up on tackling the trade border in the Irish Sea, pointing out that governments change, with a general election due next year.
“A different government may have a different position but we’re going to stay strong, we’re going to stay resilient,” he said.
Earlier this week, the SDLP submitted a recall petition for the Assembly to discuss the environmental crisis in Lough Neagh.
Mr Murphy did not indicate support for that, saying that the first step of any sitting will be the election of a Speaker, which the DUP has refused to participate in during previous recall attempts.
“We have to be in a place where the DUP agree to end their boycott of the Assembly, where the British government come to an agreement with the DUP and let us all get back to work and deal with the issues are at hand,” he said.
Mr Poots said his party have not discussed the prospect of an Assembly recall.