Tensegrity, a unique structural concept, realized by combining pre-compressed struts and pre-tensioned cables that ensure structural integrity, offers advantages such as lightweight design, deployability, and adaptability. The stability of tensegrity is contingent upon specific configurations (self-stressed state) that should ensure both global stability and address local instabilities caused due to member buckling and/or cable slacking. Existing force density-based form-finding approaches that optimized nodal coordinates in identifying the stable form, mostly overlooked the local buckling scenarios and often disregarded the tensegrity concept of dedicated forcing in the cables and struts. Moreover, such coordinate optimization-based strategies may lead to unmanageable problem formulation, especially for complex high dimensional tensegrities. To avert such challenges, in the current study, an innovative approach, considering the force density coefficients as control parameters, is investigated, while leveraging the robustness of Levenberg–Marquardt optimization to avoid ill-conditioning and singularity in the problems. The proposed algorithm demonstrates convincing outcomes, as the identified tensegrity form ensures tensegrity constraints, and overall stability while effectively mitigating local instabilities arising from cable slackening or strut buckling.