The quantum-mechanical phase of the wavefunction of an electron can be changed by electromagnetic potentials, as was predicted by Aharonov and Bohm(1) in 1959. Experiments on propagating electron waves in vacuum have revealed both the magnetic(2-4) and electrostatic(5) Aharonov-Bohm effect, Surprisingly, the magnetic effect was also observed in micrometre-sized metal rings(6-8), demonstrating that electrons keep their phase coherence in such samples despite their diffusive motion. The search for the electrostatic contribution to the electron phase in these metal rings(9,10) was hindered by the high conductivity of metal, which makes it difficult to apply a well defined voltage difference across the ring. Here we report measurements of quantum interference of electrons in metal rings that are interrupted by two small tunnel junctions, In these systems, a well defined voltage difference between the two parts of the ring can be applied, Using these rings we simultaneously explore the influence of magnetic and electrostatic potentials an the Aharonov-Bohm quantum-interference effect, and we demonstrate that these two potentials play interchangeable roles.