Population protocol (PP) is a distributed computing model for passively mobile systems, in which a computation is executed by interactions between two agents. This paper is concerned with an extended model, population protocol based on interactions of at most k agents (PPk). Beauquier et al. (2012) recently introduced the model, and showed a hierarchy of computational powers of PPk with respect to k; a PPk+1 is strictly more powerful than a PPk. Motivated by a further understanding of the model, this paper investigates the space complexity of PPk for self-stabilizing leader election (SS-LE), which is a fundamental problem for a distributed system. Cai et al. (2012) showed that the space complexity of SS-LE for n agents by a PP (i.e., PP2) is exactly n. This paper shows that the space complexity of SS-LE for n agents by a PPk is exactly ⌈(n - 1)/(k - 1)⌉ + 1.