An efficient and direct method of catalytic conversion of methane to liquid methanol and other oxygenates would be of considerable practical value. However, it remains an unsolved problem in catalysis, as typically it involves expensive or corrosive oxidants or reaction media(5-8) that are not amenable to commercialization. Although methane can be directly converted to methanol using molecular oxygen under mild conditions in the gas phase, the process is either stoichiometric (and therefore requires a water extraction step) or is too slow and low-yielding to be practical. Methane could, in principle, also be transformed through direct oxidative carbonylation to acetic acid, which is commercially obtained through methane steam reforming, methanol synthesis, and subsequent methanol carbonylation on homogeneous catalysts. However, an effective catalyst for the direct carbonylation of methane to acetic acid, which might enable the economical small-scale utilization of natural gas that is currently flared or stranded, has not yet been reported. Here we show that mononuclear rhodium species, anchored on a zeolite or titanium dioxide support suspended in aqueous solution, catalyse the direct conversion of methane to methanol and acetic acid, using oxygen and carbon monoxide under mild conditions. Here, we find that the two products form through independent pathways, which allows us to tune the conversion: three-hour-long batch-reactor tests conducted at 150 degrees Celsius, using either the zeolitesupported or the titanium-dioxide-supported catalyst, yield around 22,000 micromoles of acetic acid per gram of catalyst, or around 230 micromoles of methanol per gram of catalyst, respectively, with selectivities of 60-100 per cent. Finally, we anticipate that these unusually high activities, despite still being too low for commercial application, may guide the development of optimized catalysts and practical processes for the direct conversion of methane to methanol, acetic acid and other useful chemicals.