Appointing an independent chair to take over the faltering Stormont talks process would be a waste of time, the Ulster Unionists have claimed.
UUP leader Robin Swann rejected the call made by Sinn Fein, the SDLP and Alliance as he emerged from a meeting with the UK Prime Minister at Downing Street.
The three parties claim the UK government's role as a facilitator in negotiations to re-establish the crisis-hit institutions has been fatally undermined by the mooted parliamentary deal with the DUP.
They have demanded that Northern Ireland Secretary of State James Brokenshire step aside from chairing any part of the talks.
The head of the Northern Ireland Civil Service, Sir Malcolm McKibbin, has already taken on responsibility for moderating many of the exchanges, with Sinn Fein and the SDLP having already questioned the impartiality of Mr Brokenshire earlier in the process.
Mr Swann said talk of replacing Mr Brokenshire or appointing an independent chair from outside the UK and Ireland was a "sideshow".
"We have two weeks from today to get the Northern Ireland executive up and functioning again and to try to bring in a new chair is actually a waste of time and a distraction," he said.
"The Ulster Unionist Party is prepared, as we have always been prepared, to get the executive up and functioning again."
Northern Ireland has been without a powersharing Executive since March and without a First and Deputy First Minister since January.
The institutions collapsed amid a bitter row between the DUP and Sinn Fein about a botched green energy scheme.
The Government has warned that direct rule from London could be reimposed if the local parties fail to reach an agreement before a June 29 deadline.
All five Northern Ireland parties had separate meetings with Mrs May at No 10 on Thursday afternoon.
SDLP leader Colum Eastwood said the Prime Minister had not convinced him the "DUP tail is not wagging the Tory dog".
"We were very clear that it can't be a deal that gives the DUP power over the Tory Party," he said.
"It can't be a deal that affects and infects the talks process."
Alliance leader Naomi Long struck a more optimistic note as she left Downing Street.
"We remain optimistic that a deal (on powersharing) can be done if others have the will to do so," she said.