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The interest in producing ultrashort electron bunches has risen sharply among scientists working on the design of high-gradient wakefield accelerators. One attractive approach generating electron bunches is to illuminate a photocathode with a train of femtosecond laser pulses. In this paper we describe the design and testing of a laser system for an rf gun based on a commercial titanium-sapphire laser technology. The technology allows the production of four femtosecond laser pulses with a continuously variable pulse delay. We also use the designed system to demonstrate the experimental generation of an electron microbunch train obtained by illuminating a cesium-telluride semiconductor photocathode. We use conventional diagnostics to characterize the electron microbunches produced and confirm that it may be possible to control the main parameter of an electron microbunch train.