Doncaster and Barnsley - along with 16 other councils across the county - are backing a devolved deal for the whole of Yorkshire. But Government officials have said they will not discuss a wider deal until the South Yorkshire arrangement is signed first.
Sheffield and Rotherham are the only local authorities not pledging their support for a 'one Yorkshire deal'.
Mayor Jones and fellow Yorkshire devolution supporting council leaders joined business bosses and trade unions in York recently to 're-commit' to the plan.
But Local Government Secretary James Brokenshire reiterated the Government's stance and said they were 'not prepared' to enter discussions at present on wider devolution matters which include Sheffield City Region members.
In a letter to council leaders across Yorkshire last month, he said: "The Government has always been clear that the first step to any devolution deal across Yorkshire is the full implementation of the 2015 Sheffield City Region devolution deal."
"Until the Sheffield City Region deal is fully implemented, the Government is not prepared to enter into any discussion about wider devolution arrangements that would include some or all of the SCR authorities."
Speaking on Tuesday, Mayor Jones said she was still committed to the wider Yorkshire deal and an economic case was forthcoming.
"It's about us saying 'come on Government' what is the best deal for the people? We've got our mandate from not only from residents but also from businesses," she said.
"We believe we have the right economic footprint that sells out there and the work is being done to present all that."
When asked if the Yorkshire proposal was based on an emotional, rather than economic argument, Mayor Jones said.
"It's both and the economic argument is being pulled together - of course we've been told to get Government to look at it is for the economic argument.
"This is about different political parties coming together - different voices from the three main parties and it was great to see so many wanting to deliver.
"The work has been progressed now in order to prove to Government that it's a viable option."
Mayor Jones outlined the Sheffield City Region deal wasn't dead but Doncaster wanted assurances they wouldn't be locked into devolution arrangement indefinitely.
"What we want is a guarantee that we're part and parcel of the renegotiation of the Yorkshire deal and going on there at the first opportunity - we're prepared to talk to Government and Mr Brokenshire at any time," she said.
"We just want the assurances and others to be where they want to be. I'd be delighted if Sheffield and Rotherham want to be part of it but they need to make that decision themselves."
All four South Yorkshire councils signed a deal with the then Chancellor George Osborne for devolved powers and £900 million in cash over 30 years in 2015.
In September 2017, Doncaster and Barnsley leaders pulled out of the South Yorkshire deal, meaning that Sheffield City Region Mayor Dan Jarvis was elected in May with virtually no powers.