The adsorption of methylamine at the surface of amorphous ice is studied at various temperatures, ranging from 20 to 200 K, by grand canonical Monte Carlo simulations under conditions that are characteristic to the interstellar medium (ISM). The results are also compared with those obtained earlier on crystalline (I-h) ice. We found that methylamine has a strong ability of being adsorbed on amorphous ice, involving also multilayer adsorption. The decrease of the temperature leads to a substantial increase of this adsorption ability; thus, considerable adsorption is seen at 20-50 K even at bulk gas phase concentrations that are comparable with that of the ISM. Further, methylamine molecules can also be dissolved in the bulk amorphous ice phase. Both the adsorption capacity of amorphous ice and the strength of the adsorption on it are found to be clearly larger than those corresponding to crystalline (I-h) ice, due to the molecular scale roughness of the amorphous ice surface as well as to the lack of clear orientational preferences of the water molecules at this surface. Thus, the surface density of the saturated adsorption monolayer is estimated to be 12.6 +/- 0.4 mu mol/m(2), 20% larger than the value of 10.35 mu mol/m(2), obtained earlier for I-h ice, and at low enough surface coverages the adsorbed methylamine molecules are found to easily form up to three hydrogen bonds with the surface water molecules. The estimated heat of adsorption at infinitely low surface coverage is calculated to be -69 +/- 5 kJ/mol, being rather close to the estimated heat of solvation in the bulk amorphous ice phase of -74 +/- 7 kJ/mol, indicating that there are at least a few positions at the surface where the adsorbed methylamine molecules experience a bulk-like local environment.