Mosley's refusal to resign, or even accept a compromise agreement, in the wake of lurid allegations about his private life has amazed senior figures within the motoring organisations.
That has resulted in a letter being sent to Mosley imploring him to step down ahead of next Tuesday's confidence vote in Paris to spare the governing body further embarrassment and damage.
A section of the letter reads: "We strongly believe that the only respectable way forward for the FIA, and for yourself, is to have an orderly transition, with an immediate agreement and your commitment to step down."
The letter is signed by representatives from America (AAA and AATA), Austria (OEMTC), Belgium (TCB), Brazil (CCB), Canada (CAA), Denmark (FDM), Finland, (AL), France (FFA), Germany (ADAC), Hungary (MAK), India (FIAA), Israel (MEMSI), Japan (JAF), Singapore (AAS), Spain (RACC and RACE), Sweden (M), Switzerland (TCS) and the Netherlands (KNAC).
The clubs have also expressed their anger at Mosley for refusing the offer of a compromise deal to step down in November in exchange for a guaranteed victory in next week's vote.
The suggestion was proposed by the World Council for Automobile Mobility and Tourism (WCAMT), a senior body of the FIA.
The letter added: "We deeply regret your refusal to accept the proposal by the members of WCAMT to reach an agreement for you to step down at the General Assembly in the coming month of November.
"This is a constructive effort to facilitate an orderly transition within the FIA and to find a solution to the present crisis.
"Instead, your intention to remain until the end of your term in 2009, in spite of the severe damage being inflicted to the FIA, could imply putting personal considerations before the interests of the FIA and its member clubs."