A method of making a pliable, bioabsorbable hemostatic dressing wherein the dressing is composed of fibers with at least one molecular-scale coating, which upon first contact with blood and due to a large area of contact with blood per unit weight of active ingredients, initiates and accelerates the biochemical blood clotting cascade processes. The steps of the method include dissolving in an organic solvent one or more soluble bioabsorbable polymers and organic or aqueous-organic media of non-protein constituents to create a homogeneous mixture; forming fibers from the homogeneous mixture; adding to the fibers a molecular-scale first coating of one or more proteins of blood clotting species that minimally react with each other; and optionally adding a second coating of one or more proteins of blood clotting species to the fibers that minimally react with each other and that, together with the one or more proteins of blood clotting species in the molecular-scale first coating, induce blood coagulation in the presence of blood. The fibers may optionally have occluded in them or at their surface other chemicals of abiological or biological origin that aid in the blood clotting process.