Local Government Minister Lord Bourne told the House of Lords that devolution deals would not be imposed on areas but made clear those that wanted significant powers must have elected mayors.
He was asked about the Government’s stance as the proposed Greater Lincolnshire devolution deal looks close to collapse over Lincolnshire County Council’s opposition to the creation of a new elected mayor.
Lord Bourne said: “I have indicated that there have been deals without mayors - that was the case in Cornwall - but they were unambitious deals.
“It remains the case that, whether it is rural or urban, the most ambitious deals will have mayors.”
His intervention comes amid ongoing confusion over how Yorkshire could take on new powers from the Government in areas such as transport, planning and skills.
A deal involving South Yorkshire councils hangs in the balance amid suggestions that efforts to reach a single agreeement for the whole region could be revived in the coming weeks.