In the original operator approach to Liouville theory on the strip initiated by the second author and \textit{A. Neveu} [Nucl. Phys. B 238, 125-141 (1984)] only the simplest inverse power of the metric tensor operator could be derived. Using the quantum group structure of two- dimensional gravity recently found by the second author [Commun. Math. Phys. 138, No. 2, 301-338 (1991; Zbl 0726.17026)] the authors of the present paper derive expressions for any negative power of the metric corresponding to arbitrary representations of the underlying quantum group and check that they form a family of operators that are mutually local and closed under fusion.