The ZAZ-968 and its modifications were produced from 1971 to 1980. It featured the same 40 hp (30 kW; 41 PS) 1,197 cc (73.0 cu in) MeMZ 968 V4 as the ZAZ 966, but the exterior design was slightly modernized. The most obvious alteration was replacing the fakechrome grille in the car's front with a horizontal chrome decoration.

The 968 was discontinued in 1978, having been produced simultaneously with the newer 968A since 1973, which was produced until 1980. It introduced new safety measures, including a safer driving wheel and a plastic dashboard instead of the earlier metal one. The 968A also had its variants for the disabled (the ZAZ-968R, B, B2, AB, and AB2) with the 30 hp (22 kW; 30 PS) 887 cc (54.1 cu in) engine.

Toward the end of 1974, an up-market 968A debuted, surviving until 1979. Among its improvements were padded dash, energy-absorbing (collapsing) steering column, and seats from the VAZ-2101. The export 968E (destined mostly for the Eastern Bloc) had headlights able to meet international standards, a safety glass windscreen, and anti-theft steering lock.