Stoker, a leading lawyer, has served as deputy president for sport under Todt, while he also chairs the World Motor Sport Council.
Kristensen, a nine-time winner of Le Mans and who also serves as a steward when called upon for F1 grands prix, would step into Stoker's role if the Briton becomes the new president.
Belgian Thierry Willemarck and New Zealand’s Brian Gibbons would continue in their roles as deputy president for mobility and FIA Senate president respectively on Stoker's ticket.
Via a statement, Stoker said: “I want the FIA and our member clubs to gain global influence across all aspects of sport and mobility, emerging transport and energy trends.
“We will build on the outstanding work of president Jean Todt over the last 12 years and are proud to have been able to help introduce many new innovative programmes and resources to support members and have assisted the president in developing our clubs and building the FIA into a strong, respected and influential international organisation.
“Our core belief is an 'FIA for All' which will continue to strengthen our Federation - for our members, our sport and our society.”
Running against Stoker will be former rally driver Mohammed Ben Sulayem. They are the only two figures to announce their candidacy.
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