Generation of unbound nitric oxide (NO) via the oxidative denitrosylation (ODN) mechanism is proposed to involve the simultaneous reaction of nitrite with oxy and deoxy hemoglobin (Hb(O2) (k1) and Hb (k13)) to yield respectively, *NO2 and Hb(+2)(NO). These two reaction pathways are coupled when *NO2 reacts with Hb(+2)(NO) to yield Hb(+3)(NO) (k22), a species that releases NO rapidly. Here, I have constructed an experimentally based molecular model of the ODN mechanism (k1-k31), focusing on the high nitrite reductase activity of R-state hemoglobin. This model was used to test the hypothesis that human fetal hemoglobin (HbF) can generate unbound NO faster and to a greater extent than HbA, consequent to a 25-fold larger value of k1, which was determined in an earlier study. The results show that despite the use of identical values for k22, there was a 44-fold larger apparent rate of reaction of *NO2 with HbF(NO) compared to HbA(NO), for reactions simulated at 410 μM nitrite and 100 μM hemoglobin (heme basis), 50% oxygen saturation at pH 7.4 and 37°C. This faster reaction was associated with the generation of about 11 μM peak unbound NO. In contrast, HbA failed to generate unbound NO rapidly under the same conditions. However, raising the concentration of nitrite into the millimolar range did generate unbound NO in the HbA simulation, in agreement with the experimental literature, and that result was associated with acceleration in the rate of reaction of NO2 with HbA(NO). Unbound NO could be generated at 410 μM nitrite in the HbA simulation by lowering the pH. This too was associated with an acceleration in the rate of reaction of NO2 with HbA(NO). Furthermore, generation of unbound NO could be assigned to the pH-dependent increase in k1, independent of the associated increase in k(13). Finally, selective exchange of the HbA value of k1 for the HbF value, keeping all other constants and conditions unchanged, generated kinetic patterns for the various species of the "k1-modified" HbA simulation, which were virtually indistinguishable from those seen in the HbF simulation. Taken together, these findings show that rapid and extensive generation of unbound NO within the ODN mechanism is controlled by the value of k1. The faster and more extensive generation of unbound NO by HbF at micromolar nitrite concentration suggests a possible second function for HbF in sickle cell disease, namely enhanced vasodilation. The failure of 410 μM nitrite to generate unbound NO in the HbA simulation at pH 7.4, contrasts with evidence in the literature showing that exposure of intact red cells to 100 to 200 μM nitrite in PBS, promoted NO release into the gas phase. I point out that this difference in outcome may be due to the higher activity of HbA when bound to the cytoplasmic domain of the red cell membrane anion transport protein SLC4A1 (band 3) and to the demonstrated capacity of band 3 to transport nitrite.