In this article we propose an algebraic universal procedure for deriving the fusion rules and the Baxter equation for any integrable model with U q (sl 2 ) symmetry by means of the quantum inverse scattering method. The universal BaxterQ -operator is obtained from a certain infinite dimensional representation called q-oscillator representation of the universalR -matrix for the U q (sl 2 ) affine algebra (first proposed by V. Bazhanov, S. Lukyanov and A. Zamolodchikov [hep-th/9604044] for the quantum KdV case). We also examine the algebraic properties of the Q-operator.