We study the beam-energy and system-size dependence of φ meson production (using the hadronic decay mode φ → K + K − ) by comparing the new results from Cu+Cu collisions and previously reported Au+Au collisions at √ s NN = 62.4 and 200 GeV measured in the STAR experiment at RHIC. Data presented are from midrapidity (|y| <0.5) for 0.4 < p T < 5 GeV/c. At a given beam energy, the transverse momentum distributions for φ mesons are observed to be similar in yield and shape for Cu+Cu and Au+Au colliding systems with similar average numbers of participating nucleons. The φ meson yields in nucleus-nucleus collisions, normalised by the average number of participating nucleons, are found to be enhanced relative to those from p+p collisions with a different trend compared to strange baryons. The enhancement for φ mesons is observed to be higher at √ s NN = 200 GeV compared to 62.4 GeV. These observations for the produced φ(ss) mesons clearly suggest that, at these collision energies, the source of enhancement of strange hadrons is related to the formation of a dense partonic medium in high energy nucleus-nucleus collisions and cannot be alone due to canonical suppression of their production in smaller systems.