A Lie group $G$ in a group pair $(D,G)$, integrating the Lie algebra ${\mathfrak g}$ in a Manin pair $({\mathfrak d}, {\mathfrak g})$, has a quasi-Poisson structure. We define the quasi-Poisson actions of such Lie groups $G$, and show that they generalize the Poisson actions of Poisson Lie groups. We define and study the moment maps for those quasi-Poisson actions which are hamiltonian. These moment maps take values in the homogeneous space $D/G$. We prove an analogue of the hamiltonian reduction theorem for quasi-Poisson group actions, and we study the symplectic leaves of the orbit spaces of hamiltonian quasi-Poisson spaces.