The Odin satellite has been used to search for the 118.75-GHz line of molecular oxygen (O_2) in the Galactic centre. Odin observations were performed towards the Sgr A* circumnuclear disk (CND), and the Sgr A +20 km s-1 and +50 km s-1 molecular clouds using the position-switching mode. Supplementary ground-based observations were carried out in the 2-mm band using the ARO Kitt Peak 12-m telescope to examine suspected SiC features. A strong emission line was found at 118.27 GHz, attributable to the J=13-12 HC_3N line. Upper limits are presented for the 118.75-GHz O_2 (1_1-1_0) ground transition line and for the 118.11-GHz 3\Pi_2, J=3-2 ground state SiC line at the Galactic centre. Upper limits are also presented for the 487-GHz O_2 line in the Sgr A +50 km s-1 cloud and for the 157-GHz, J=4-3, SiC line in the Sgr A +20 and +50 km s-1 clouds, as well as the CND. The CH_3OH line complex at 157.2 - 157.3 GHz has been detected in the +20 and +50 km s-1 clouds but not towards Sgr A*/CND. A 3 sigma upper limit for the fractional abundance ratio of [O_2]/[H2] is found to be X(O_2) <= 1.2 * 10-7 towards the Sgr A molecular belt region.