Context. The multiplicity of classical Cepheids (CCs) and RR Lyrae stars (RRLs) is still imperfectly known, particularly for RRLs. Aims. In order to complement the close-in short orbital period systems presented in Paper I, our aim is to detect the wide, spatially resolved companions of the targets of our reference samples of Galactic CCs and RRLs. Methods. Angularly resolved common proper motion pairs were detected using a simple progressive selection algorithm to separate the most probable candidate companions from the unrelated field stars. Results. We found 27 resolved, high probability gravitationally bound systems with CCs out of 456 examined stars, and one unbound star embedded in the circumstellar dusty nebula of the long-period Cepheid RS Pup. We found seven spatially resolved, probably bound systems with RRL primaries out of 789 investigated stars, and 22 additional candidate pairs. We report in particular new companions of three bright RRLs: OV And (companion of F4V spectral type), RR Leo (M0V), and SS Oct (K2V). In addition, we discovered resolved companions of 14 stars that were likely misclassified as RRLs. Conclusions. The detection of resolved non-variable companions around CCs and RRLs facilitates the validation of their Gaia DR2 parallaxes. The possibility to conduct a detailed analysis of the resolved coeval companions of CCs and old population RRLs will also be valuable to progress on our understanding of their evolutionary path.
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