Let \(\Sigma\) be a closed 2-dimensional Riemannian manifold, let \(N\) be an \(n\)-dimensional compact Riemannian manifold isometrically embedded into \(\mathbb{R}^\ell\). For a smooth 2-form \(\omega\) on \(N\) and \(u\in H^{1,2} (\Sigma,N)\) define \[ I_\omega(u)= {\textstyle {\frac12}} \int_\Sigma|\nabla u|^2 dV_\Sigma+2 \int_\Sigma u^*\omega. \] In the case of \(d\omega=0\) the Euler-Lagrange equation of \(I_\omega\) is the harmonic map equation. If \(u\) is a conformal solution of the Euler-Lagrange equation, then \(u\) describes a surface in \(N\) of prescribed mean curvature given by \(d\omega\). The main result says that under certain conditions there exists a local minimizer for \(I_\omega\) in a given homotopy class. More precisely, there is a constant \(C>0\) such that for \(u_0\in H^{1,2}(\Sigma,N)\) and a smooth extension \(\widetilde{\omega}\) of \(\omega\) to \(\mathbb{R}^\ell\) satisfying \(|d\widetilde{\omega} |\cdot\int_\Sigma|\nabla u_0|^2 dV_\Sigma