We develop a functional renormalization group approach which describes the low-energy single-particle properties of the Anderson impurity model up to intermediate on-site interactions [Formula: see text], where Δ is the hybridization in the wide-band limit. Our method is based on a generalization of a method proposed by Schütz et al (2005 Phys. Rev. B 72 035107), using two independent Hubbard-Stratonovich fields associated with transverse and longitudinal spin fluctuations. Although we do not reproduce the exponentially small Kondo scale in the limit [Formula: see text], the spin fluctuations included in our approach remove the unphysical Stoner instability predicted by mean field theory for U>πΔ. We discuss different decoupling schemes and show that a decoupling which manifestly respects the spin-rotational invariance of the problem gives rise to the lowest quasiparticle weight. To obtain a closed flow equation for the fermionic self-energy we also propose a new scheme of truncation of the functional renormalization group flow equations using Dyson-Schwinger equations to express bosonic vertex functions in terms of fermionic ones.