Fix a spherically symmetric wavelet \(\psi\) satisfying an admissibility condition and, as usual, for any \(b\in\mathbb R^n\) and \(a>0\), denote \(\psi^{a,b}(x) = a^{-n/2}\psi(\frac{x-b}{a})\). The continuous wavelet transform of a compactly supported distribution \(f\) associated to \(\psi\) is given by \((Tf)(a,b)= \langle f,\overline{\psi^{a,b}}\rangle\). Assume that \(f\in {\mathcal E}'(\mathbb R^n)\) also belongs to the Sobolev space \(H^{-l}(\mathbb R^n)\), \(l>0\). The main theorem of the present paper states that, if \(s\geq(n-1)/2+l\), then \[ \lim_{\lambda\to 0+}W^s_{\lambda}f(x) = 0 \] uniformly with respect to \(x\in K\) for any compact subset \(K\subset\mathbb R^n\setminus \operatorname{supp}f\). Here, \[ W^s_\lambda f(x)= C_\psi^{-1} \int_{a>\lambda} \bigg(1-\frac{\lambda^2}{a^2}\bigg)^s \frac{da}{a^{n+1}} \int_{\mathbb R^n}(Tf)(a,b) \psi^{a,b}(x)\,db \] is the Riesz means of order \(s\) of the partial wavelet transforms and \(C_\psi\) is a constant related to the admissibility condition.