Localization of cardiac anatomical landmarks is an important step towards a more robust and accurate analysis of the heart. A fully automatic hybrid framework is proposed that detects key landmark locations in cardiac magnetic resonance (MR) images. Our method is trained and evaluated for the detection of mitral valve points on long-axis MRI and RV insert points in short-axis MRI. The framework incorporates four key modules for the localization of the landmark points. The first module crops the MR image around the heart using a convolutional neural network (CNN). The second module employs a U-Net to obtain an efficient feature representation of the cardiac image, as well as detect a preliminary location of the landmark points. In the third module, the feature representation of a cardiac image is processed with a Recurrent Neural Network (RNN). The RNN leverages either spatial or temporal dynamics from neighboring slides in time or space and obtains a second prediction for the landmark locations. In the last module the two predictions from the U-Net and RNN are combined and final locations for the landmarks are extracted. The framework is separately trained and evaluated for the localization of each landmark, it achieves a final average error of 2.87 mm for the mitral valve points and an average error of 3.64 mm for the right ventricular insert points. Our method shows that the use of a recurrent neural network for the modeling of additional temporal or spatial dependencies improves localization accuracy and achieves promising results.