We generate a molecular beam of ice nanoparticles (H2O)N, N̅ ≈ 130-220, which picks up several individual gas phase uracil (U) or 5-bromouracil (BrU) molecules. The mass spectra of the doped nanoparticles prove that the uracil and bromouracil molecules coagulate to clusters on the ice nanoparticles. Calculations of U and BrU monomers and dimers on the ice nanoparticles provide theoretical support for the cluster formation. The (U)mH+ and (BrU)mH+ intensity dependencies on m extracted from the mass spectra suggest a smaller tendency of BrU to coagulate compared to U, which is substantiated by a lower mobility of bromouracil on the ice surface. The hydrated Um·(H2O)nH+ series are also reported and discussed. On the basis of comparison with the previous experiments, we suggest that the observed propensity for aggregation on ice nanoparticles is a more general trend for biomolecules forming strong hydrogen bonds. This, together with their mobility, leads to their coagulation on ice nanoparticles which is an important aspect for astrochemistry.