A class of general linear overparameterized systems with fully unknown parameters affected by unknown but bounded perturbation is considered under the condition that only the system output is measurable. An adaptive observer augmented with a high-gain disturbance estimator is proposed to reconstruct states of the above-mentioned systems, which, unlike known state and disturbance observers, (i) does not require the system parameters to be known, (ii) does not use the internal model principle, (iii) overcomes strictly-positive-real/relative degree one/output matching restrictions, (iv) reconstructs the system physical states instead of the virtual ones of its observer canonical form, (v) ensures asymptotic convergence of both the parametric and state observation errors to zero. Unlike existing approaches, the proposed solution needs to satisfy novel weak integrability/non-integrability conditions for some signals. Obtained theoretical results are validated via numerical simulations.