In case of a release of hazardous radioactive matter to the atmosphere from e.g., a nuclear power plant accident, atmospheric dispersion models are used to predict the spatial distribution of radioactive particles and gasses. However, at the early stages of an accident, only limited information about the release may be available. Thus, there is a need for source term estimation methods suitable for operational use shortly after an accident. We have developed a Bayesian inverse method for estimating the multi-nuclide source term describing a radioactive release from a nuclear power plant. The method provides a probabilistic source term estimate based on the early available observations of air concentration and gamma dose rate by monitoring systems. The method is intended for operational use in case of a nuclear accident, where no reliable source term estimate exists. We demonstrate how the probabilistic formulation can be used to provide estimates of the released amounts of each radionuclide as well as estimates of future gamma dose rates. The method is applied to an artificial case of a radioactive release from the Loviisa nuclear power plant in southern Finland, considering the most important dose-contributing nuclides. The case demonstrates that only limited air concentration measurement data may be available shortly after the release, and that to a large degree one will have to rely on gamma dose rate observations from a frequently reporting denser monitoring network. Further, we demonstrate that information about the core inventory of the nuclear power plant can be used to constrain the release rates of certain radionuclides, thereby decreasing the number of free parameters of the source term.