About half of human cancers are associated with mutations of the tumor suppressor p53. Gained oncogenic functions of the mutants have been related to aggregation behaviors of wild-type and mutant p53. The thermodynamic and kinetic mechanisms of p53 aggregation are poorly understood. Here we find that wild-type p53 forms an anomalous liquid phase. The liquid condensates exhibit several behaviors beyond the scope of classical phase transition theories: their size, ca. 100 nm, is independent of the p53 concentration and decoupled from the protein mass held in the liquid phase. Furthermore, the liquid phase lacks constant solubility. The nucleation of p53 fibrils deviates from the accepted mechanism of sequential association of single solute molecules. We find that the liquid condensates serve as pre-assembled precursors of high p53 concentration that facilitate fibril assembly. Fibril nucleation hosted by precursors represents a novel biological pathway, which opens avenues to suppress protein fibrillation in aggregation diseases.