Drug repurposing studies targeting inhibition of RNA dependent RNA polymerase (RdRP) of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) have exhibited the potential effect of small molecules. In the present work a detailed interaction study between the phytochemicals from Indian medicinal plants and the RdRP of SARS-CoV-2 has been performed. The top four phytochemicals obtained through molecular docking were, swertiapuniside, cordifolide A, sitoindoside IX, and amarogentin belonging to Swertia chirayita, Tinospora cordifolia and Withania somnifera. These ligands bound to the RdRP were further studied using molecular dynamics simulations. The principal component analysis of these systems showed significant conformational changes in the finger and thumb subdomain of the RdRP. Hydrogen bonding, salt-bridge and water mediated interactions supported by MM-GBSA free energy of binding revealed strong binding of cordifolide A and sitoindoside IX to RdRP. The ligand-interacting residues belonged to either of the seven conserved motifs of the RdRP. These residues were polar and charged amino acids, namely, ARG 553, ARG 555, ASP 618, ASP 760, ASP 761, GLU 811, and SER 814. The glycosidic moieties of the phytochemicals were observed to form favourable interactions with these residues. Hence, these phytochemicals may hold the potential to act as RdRP inhibitors owing to their stability in binding to the druggable site.