Searches for new heavy resonances decaying to WW, WZ, and ZZ bosons are presented, using a data sample corresponding to 3.2 fb−1 of pp collisions at s=13 TeV collected with the ATLAS detector at the CERN Large Hadron Collider. Analyses selecting ννqq, ℓνqq, ℓℓqq and qqqq final states are combined, searching for an arrow-width resonance with mass between 500 and 3000 GeV. The discriminating variable is either an invariant mass or a transverse mass. No significant deviations from the Standard Model predictions are observed. Three benchmark models are tested: a model predicting the existence of a new heavy scalar singlet, a simplified model predicting a heavy vector-boson triplet, and a bulk Randall-Sundrum model with a heavy spin-2 graviton. Cross-section limits are set at the 95% confidence level and are compared to theoretical cross-section predictions for a variety of models. The data exclude a scalar singlet with mass below 2650 GeV, a heavy vector-boson triplet with mass below 2600 GeV, and a graviton with mass below 1100 GeV. These results significantly extend the previous limits set using pp collisions at s=8 TeV.[Figure not available: see fulltext.]