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• We derive the mild solution of the damped fractional integrodifferential system in terms of Riemann-Liouville fractional resolvent, where and is a real number. • We prove the existence and uniqueness of mild solutions of the system using generalized fixed point theorem. • We prove the approximate controllability of the system using iterative and approximate technique. For this, we prove the Lemma 4.3. This article is concerned with Riemann-Liouville fractional semilinear integrodifferential systems with damping in Banach spaces. First we prove the existence of mild solutions of the system using fixed point approach, then we establish new sufficient conditions for the approximate controllability of the system by means of iterative and approximate technique. To obtain our results, we use the concept of Riemann-Liouville fractional (ϑ, φ, λ) resolvent, where 0 < φ < ϑ ≤ 1 and λ is a real number. Finally, an example is provided for the illustration of the obtained results. [ABSTRACT FROM AUTHOR]