MgB2 ultrathin films have potential to make sensitive superconducting devices such as superconducting single-photon detectors working at relatively high temperatures. We have grown epitaxial MgB2 films in thicknesses ranging from about 40 nm to 6 nm by using the hybrid physical-chemical vapor deposition method and performed electrical transport measurements to study the thickness dependence of the superconducting critical temperature T-c. With reducing film thickness d, although a weak depression of the T-c has been observed, which could be attributed to an increase of disorder (interband impurity scattering) in the film, the T-c retains close to the bulk value of MgB2 (39 K), being about 35 K in the film of 6 nm thick. We show that this result, beneficial to the application of MgB2 ultrathin films and in accordance with recent theoretical calculations, is in contrast to previous findings in MgB2 films prepared by other methods such as co-evaporation and molecular-beam epitaxy, where a severe T-c suppression has been observed with T-c about one third of the bulk value in films of similar to 5 nm thick. We discuss this apparent discrepancy in experiments and suggest that, towards the ultrathin limit, the different degrees of T-c suppression displayed in currently obtained MgB2 films by various techniques may arise from the different levels of disorder present in the film or different extents of proximity effect at the film surface or film-substrate interface. (C) 2013 AIP Publishing LLC.