The X-ray transient XTE J1719-291 was discovered with Rossi X-ray Timing Explorer/Proportional Counter Array (RXTE/PCA) during its outburst in 2008 March, which lasted at least 46 d. Its 2-10 keV peak luminosity is 7 × 1035 erg s-1 assuming a distance of 8 kpc, which classifies the system as a very faint X-ray transient. The outburst was monitored with Swift, RXTE, Chandra and XMM-Newton. We analysed the X-ray spectral evolution during the outburst. We fitted the overall data with a simple power-law model corrected for absorption and found that the spectrum softened with decreasing luminosity. However, the XMM-Newton spectrum cannot be fitted with a simple one-component model, but it can be fitted with a thermal component (blackbody or disc blackbody) plus a power-law model affected by absorption. Therefore, the softening of the X-ray spectrum with decreasing X-ray luminosity might be due to a change in photon index or alternatively it might be due to a change in the properties of the soft component. Assuming that the system is an X-ray binary, we estimated a long-term time-averaged mass accretion rate of ?˜ 7.7 × 10-13 M&sun; yr-1 for a neutron star as a compact object and ?˜ 3.7 × 10-13 M&sun; yr-1 in the case of a black hole. Although no conclusive evidence is available about the nature of the accretor, based on the X-ray/optical luminosity ratio we tentatively suggest that a neutron star is present in this system.