Oceanic crust is created by the extraction of molten rock from underlying mantle at the seafloor 'spreading centres' found between diverging tectonic plates. Modelling studies have suggested that mantle melting can occur through decompression as the mantle flows upwards beneath spreading centres(1), but direct observation of this process is difficult beneath the oceans. Continental rifts, however-which are also associated with mantle melt production-are amenable to detailed measurements of their short-term kinematics using geodetic techniques. Here we show that such data can provide evidence for an upwelling mantle flow, as well as information on the dimensions and timescale of mantle melting. For North Island, New Zealand, around ten years of campaign and continuous GPS measurements in the continental rift system known as the Taupo volcanic zone reveal that it is extending at a rate of 6-15 millimetres per year. However, a roughly 70-kilometre-long segment of the rift axis is associated with strong horizontal contraction and rapid subsidence, and is flanked by regions of extension and uplift. These features fit a simple model that involves flexure of an elastic upper crust, which is pulled downwards or pushed upwards along the rift axis by a driving force located at a depth greater than 15 kilometres. We propose that flexure is caused by melt-induced episodic changes in the vertical flow forces that are generated by upwelling mantle beneath the rift axis, triggering a transient lower-crustal flow. A drop in the melt fraction owing to melt extraction raises the mantle flow viscosity and drives subsidence, whereas melt accumulation reduces viscosity and allows uplift-processes that are also likely to occur in oceanic spreading centres.