We describe a Ti:sapphire-based laser-x-ray system specifically designed for generation of ultrafast x-ray pulses in the tenths-of-nanometers spectral range at a 2-kHz repetition rate. To obtain high-contrast laser pulses we divide the laser system into a section for generation of microjoule, high-contrast pulses with pulse cleaning and a subsequent section for chirped-pulse amplification and pulse compression. This laser section operates in conjunction with an x-ray-generation section based on a moving copper wire in a He atmosphere. The high reliability of the entire system permits maintenance-free production of x-ray pulses over tens of hours. Average x-ray fluxes of 10(13) photons/(s 4pi sr 1 keV) at 3 keV and 10(9) photons/(s 4pi sr) above 5 keV of photon energy are produced.