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We study existence and Besov regularity of densities for solutions to stochastic differential equations with Hölder continuous coefficients driven by a d-dimensional Lévy process Z = (Z(t))≥0, where, for t > 0, the density function f of Z(t) exists and satisfies, for some (α)=1 ⊂ (0, 2) and C > 0, lim sup t/α ||f (z + eh) − f (z)|| dz ≤ C|h|, h ∈ R, i = 1,..., d. t→0 Here e1,..., e denote the canonical basis vectors in R. The latter condition covers anisotropic (α,..., α)-stable laws but also particular cases of subordinate Brownian motion. To prove our result we use some ideas taken from (J. Funct. Anal. 264 (2013), 1757-1778).