The cross sections of the ⁷⁰Zn(n,γ)⁷¹Znm (T1/2 = 3.96±0.05 hrs) reaction have been measured relative to the ¹⁹⁷Au(n,γ)¹⁹⁸Au cross sections at 0.96 and 1.69 MeV using a ⁷Li(p,n)⁷Be neutron source and activation technique. The cross section of this reaction has been measured for the first time in the MeV region. The new experimental cross sections have been compared with the theoretical prediction by TALYS-1.6 with various level density models as well as the TENDL-2015 library. The generalized superfluid level density model predicted the new experimental cross sections at both incident energies. The ⁷⁰Zn(n,γ)⁷¹Zng+m total capture cross sections have also been derived by applying the evaluated isomeric ratios in the TENDL-2015 library to the measured partial capture cross sections. The spectrum averaged total capture cross sections derived in the present work agree well with the JENDL-4.0 library at 0.96 MeV whereas it lies between the TENDL-2015 and JENDL-4.0 libraries at 1.69 MeV. This experimental work has been also published as Phys. Rev. C 95 (2017) 024619.