SARASOTA COUNTY — With a set of heavy hearts — and some degree of broken trust — the Sarasota County Commission unanimously voted Tuesday to offer the city of North Port $2 million for its half of the Warm Mineral Springs Day Spa.

Commissioner Christine Robinson drafted the offer and presented it to the county board Tuesday. The proposal was in response to the North Port City Commission’s decision last month to sell the 81-acre Springs, which it jointly purchased with the county for $5.5 million in December 2010. The city’s decision to sell came after it decided not to approve an invitation to negotiate, or ITN, that would combine a request for proposals for short-term operations of the Springs with a transition to a proposed longer-term agreement and establishment for future operations. The invitation was unanimously approved by both the city and county commissions in a joint meeting last July, before two incumbent city commissioners were voted out. County commissioners were confused and frustrated by the city’s turnaround.