Let \(X\) be a reflexive Banach space with dual space \(X^\ast\) and let \(N_{i}:X\times X\to X^\ast\), \(\phi:X^\ast\to X^\ast\), \(\eta:X\times X\to X\), \(g:X\to X\) be single valued mappings. Also, let \(P_i,G_i,T_i:X\to CB(X)\) \((i=1,\dots,l)\) be set valued mappings and let \(H:X\to X^\ast\) be a strictly \(\eta\)-monotone mapping and \(M:X\to 2^{X^\ast}\) be a \((H,\eta,\phi)\)-monotone mapping. If \(\rho_1,\dots,\rho_{l}\), are positive constants then, under suitable assumptions and using proximal point operator techniques, the author provides necessary and sufficient conditions so that the following system of nonlinear variational type inclusions \begin{align*} 0&\in H(g(x_1))-H(g(x_2))+\rho_1[N_1(u_1,v_1)+M(g(x_1),w_1)],\\ 0&\in H(g(x_2))-H(g(x_3))+\rho_2[N_1(u_2,v_2)+M(g(x_2),w_2)],\\ &\vdots\\ 0&\in H(g(x_{l-1}))-H(g(x_{l}))+\rho_{l-1}[N_1(u_{l-1},v_{l-1})+M(g(x_{l-1}),w_{l-1})],\\ 0&\in H(g(x_{l}))-H(g(x_1))+\rho_{l}[N_1(u_{l},v_{l})+M(g(x_{l}),w_{l})], \end{align*} has a unique solution \((x_{i},u_{i},v_{i},w_{i})\) where \(x_{i}\in X\), \(u_{i}\in T_{i}(x_1)\), \(v_{i}\in G_{i}(x_1)\), \(w_{i}\in P_{i}(x_1)\) \((i=1,\dots,l)\). Moreover, an iterative algorithm for the above system is suggested and the convergence of the iterative sequences generated by the algorithm is studied.