Context. We present the results of a multi-year monitoring campaign of the Galactic center (GC) with the MAGIC telescopes. These observations were primarily motivated by reports that a putative gas cloud (G2) would be passing in close proximity to the super-massive black hole (SMBH), associated with Sagittarius A*, located at the center of our galaxy. This event was expected to give astronomers a unique chance to study the effect of in-falling matter on the broad-band emission of a SMBH. Aims. We search for potential flaring emission of very-high-energy (VHE; >= 100 GeV) gamma rays from the direction of the SMBH at the GC due to the passage of the G2 object. Using these data we also study the morphology of this complex region. Methods. We observed the GC region with the MAGIC Imaging Atmospheric Cherenkov Telescopes during the period 2012-2015, collecting 67 h of good-quality data. In addition to a search for variability in the flux and spectral shape of the GC gamma-ray source, we use a point-source subtraction technique to remove the known gamma-ray emitters located around the GC in order to reveal the TeV morphology of the extended emission inside that region. Results. No effect of the G2 object on the VHE gamma-ray emission from the GC was detected during the 4 yr observation campaign. We confirm previous measurements of the VHE spectrum of Sagittarius A*, and do not detect any significant variability of the emission from the source. Furthermore, the known VHE gamma-ray emitter at the location of the supernova remnant G0.9+0.1 was detected, as well as the recently discovered VHE source close to the GG radio arc.