The two authorities are looking at linking up to provide shared services and senior management after it emerged both would face financial pressures in the future.
John Williams, of the Deane, and West Somerset's Tim Taylor yesterday (Wednesday, October 23) met Secretary of State Eric Pickles and Local Government Minister Brandon Lewis in London.
Cllr Duncan McGinty, leader of Sedgemoor District Council also attended, although Cllr John Osman, leader of Somerset County Council, was unavailable.
West Somerset and Taunton Deane have prepared a business case prior to a final decision on November 12.
After the meeting, Mr Williams said: “Ministers wanted reassurance as to local commitment to this ground-breaking project, which we gave.
"We also gave the assurance that we are fully prepared to take up the proposals in the business case to look ever wider and deeper for shared services that would bring even greater savings and benefits to participating councils in Somerset.”
Mr Taylor said: “We reassured Ministers that the business case stacks up and will make savings for both councils.
"It will not provide the complete answer to the financial challenges we face but it will provide us with far greater resilience and increased capacity while helping to maintain important front line services.”