State-of-the-art algorithms for accelerated magnetic resonance image (MRI) reconstruction are nowadays dominated by deep learning-based techniques. However, the majority of these methods require the respective sampling patterns in training, which limits their application to a specific problem class. We propose an iterative reconstruction approach that incorporates the implicit prior provided by a generative adversarial network (GAN), which learns the probability distribution of uncorrupted MRI data in an off-line step. Since the unsupervised training of the GAN is completely independent of the measurement process, our method is in principle able to address multiple sampling modalities using a single pre-trained model. However, it turns out that the desired target images potentially lie outside the range space of the learned GAN, leading to reconstructions that resemble the target images only at a coarse level of detail. To overcome this issue, we propose a refinement scheme termed GAN prior adaption, that allows for additional adaption of the generating network with respect to the measured data. The proposed method is evaluated on multi-coil knee MRI data for different acceleration factors and compared to a classical as well as a deep learning-based approach showing promising quantitative and qualitative results.