The British government must not "subcontract" its role in restoring powersharing the DUP said.
Party leader Arlene Foster said there was a part for independent mediation in helping break the 20-month impasse at Stormont.
She met Prime Minister Theresa May in London on Wednesday as the British government explores convening fresh political talks.
Mrs Foster said: "We believe there's a role for facilitation but we also believe the British must not subcontract their role, because of course under the Belfast agreement until the people of Northern Ireland decided otherwise, the United Kingdom government is in charge of Northern Ireland."
She held a "detailed" meeting with the prime minister about decision-making in the north in the absence of an executive in Belfast following serious disagreements between former coalition partners the DUP and Sinn Féin.
Powersharing collapsed early last year in a row over the DUP's handling of the botched RHI green energy scheme and the dispute over identity issues like the Irish language has seen repeated rounds of negotiations fail.
Secretary of State Karen Bradley met the five main Stormont parties this week as she contemplates another push for agreement and is seeking their views about external facilitation.
Sinn Féin has been intensely critical of the British government.
Independent mediators helped previous rounds of political progress in Northern Ireland, including brokering the Good Friday Agreement 20 years ago.
Mrs Foster said civil service decision-making should be quickly rolled out amid the political paralysis.
"There is a whole range of decisions that need to be taken in Northern Ireland very, very urgently and we want to see that happening quickly," she said.
Detailed meeting with the Prime Minister today. Discussing the need for decision making in NI. While SF continue to boycott the Assembly, we continue to push for good governance. The people of NI deserve better. pic.twitter.com/NJurSLJUuj
— Arlene Foster (@DUPleader) September 12, 2018
Good governance? Really?
— Naomi Long MLA (@naomi_long) September 12, 2018
After all the revelations of the last few weeks how can they have the brass neck to tweet this?
This account is now just engaged in professional level trolling of the NI public.
We absolutely do deserve better...than this. https://t.co/ccYGfIM2S3
British & Irish governments told me the DUP did a deal with SF in February. The DUP’s own people told me this also. The leadership could not sell the agreement. RHI: experientia docet populos. Is it not risible for the DUP to state “we continue to push for GOOD governance?” https://t.co/TmOE7hr07J
— Eamonn Mallie (@EamonnMallie) September 12, 2018
Asked about talks, Mrs Foster said the "first thing we have to get set in motion" was putting in place decision-making.
Deputy leader Nigel Dodds said there must be a "full commitment to the continuing delivery of all the money that's coming to Northern Ireland" under the confidence and supply arrangements.
Mrs Bradley is planning to cut assembly members' pay and will bring forward legislation giving greater clarity around civil servants' powers to make decisions in the absence of a functioning Executive.
Meanwhile, Sinn Féin vice-president Michelle O'Neill met Irish foreign affairs minister Simon Coveney in Dublin and said it was disgraceful an executive was not in place.
She added: "The reason we have not had it is because of the British government and their toxic relationship with the DUP."
She said the Tories had prioritised the survival of its minority government and its arrangement with the DUP.
"We have been fairly firm in the belief that all along their plan was to do nothing and now I am even more concerned because I believe their plan is to prevent the restoration of the executive," she said.