A mayor serving a two-year term has been proposed as a way forward for a South Yorkshire devolution.
All four leaders are continuing to discuss the 30-year plan for £900m and devolved powers, ahead of elections for a metro-mayor in May.
Barnsley and Doncaster want to pull out of the South Yorkshire deal to pursue a wider Yorkshire deal.
Sheffield Council leader Julie Dore said: “We suggested shortening the first mayoral term to two years in the discussions last summer, which would also have the benefit of bringing South Yorkshire in line with the other mayoral elections around the country.”
Ros Jones, Mayor of Doncaster, said: “In December, people in Doncaster voted overwhelmingly in favour of pursuing a wider Yorkshire devolution agreement.
“We are now working with colleagues from across the region and Government to deliver that ambition.
“Last week 17 council leaders from across the county met and were united in reaffirming their support for the widest possible devolution agreement for Yorkshire, welcoming the new approach taken by Government. The leaders expressed their confidence that progress is being made towards securing a deal which would deliver a directly elected Mayor for Yorkshire by 2020. In the meantime, we have always said that we are willing to consider interim solutions for the Sheffield City Region and we are engaging with the Government and other councils in South Yorkshire as to how this can be achieved.”
In December, communities secretary Sajid Javid said if Barnsley and Doncaster agreed the South Yorkshire deal they could leave in 2022, if all the councils in the rest of Yorkshire agreed.
But Sir Steve Houghton of Barnsley and Mrs Jones said they wanted to be allowed to leave in 2020.
Northern Powerhouse minister Jake Berry said South Yorkshire’s deal had been signed by the leaders three times and enacted in Parliament. He said an election was happening because it was the ‘law of the land’.