We propose a technique for the production of attosecond X-ray pulses which is based on the use of X-ray SASE FEL combined with a femtosecond laser system. A few-cycle optical pulse from a Ti:sapphire laser interacts with the electron beam in a two-period undulator resonant to 800 nm wavelength and produces energy modulation within a slice of the electron bunch. Following the energy modulator the electron beam enters the X-ray undulator and produces SASE radiation. Due to energy modulation the frequency is correlated to the longitudinal position within the few-cycle-driven slice of SASE radiation pulse. The largest frequency offset corresponds to a single-spike pulse in the time domain which is confined to one half-oscillation period near the central peak electron energy. The selection of single-spike pulses is achieved by using a crystal monochromator after the X-ray undulator. Our studies show that the proposed technique is capable to produce 300-as long single pulses with GW-level output power in the 0.1 nm wavelength range, and is applicable to the European X-Ray Laser Project XFEL and the Linac Coherent Light Source at SLAC. (C) 2004 Elsevier B.V. All rights reserved.