Sir Steve Houghton of Barnsley and Ros Jones of Doncaster issued a joint statement saying they were not “intent on immediately disbanding” the Combined Authority and would consider “interim” options.
But “it must not divert us from our key priority.”
They added: “We will work with our colleagues across this great county, to secure a One Yorkshire devolution agreement with Government. Everything else should follow from that.”
The rare statement comes after weeks of pressure to stick with the deal they signed up to in October 2015 for £900m, new powers and an elected mayor.
But cracks in the relationship emerged after a successful campaign to move the HS2 station from Meadowhall to Sheffield city centre.
The statement said: “By uniting with colleagues from across the region it is clear that the prize is now within our grasp. Critically, the Government has also indicated that it is listening.
“Seventeen authorities are already involved, representing more than four million of Yorkshire’s residents. We hope that this will soon become a full complement of Yorkshire’s 20 authorities, with everyone in Yorkshire benefiting from new decision making powers and funding devolved from Whitehall.”
Their ambition appears to fly in the face of comments by the Chancellor Philip Hammond who last week said Sheffield had to be at the table in any One Yorkshire arrangement. Sheffield leader Julie Dore said her focus would be on keeping Sheffield moving forward if a deal collapsed.
The statement adds: “The cross party consensus has also demonstrated that local politicians - far from conforming to the tribal stereotype so often portrayed - are quite willing and able to work together for the greater good.”
The leaders meet to decide the future of devolution in a special meeting on Monday.