This is a reference request.

A theorem of Hurewicz (unfortunately published in the hard-to-get journal Proc.Akad. Wetensch. Amsterdam 1936) asserts $\left[X,Y\right]=Hom(\pi_1X,\pi_1Y)/Inn(\pi_1Y)$ for aspherical spaces.

The generalization to arbitrary (pairs of) spaces reads: when $f,g:(X,X_1)\rightarrow (Y,Y_1)$ are such that $f_\ast=g_\ast:\pi_i(X)\rightarrow \pi_i(Y)$ and $f_\ast=g_\ast:\pi_i(X_1)\rightarrow \pi_i(Y_1)$ for all $i$, then $f$ and $g$ are homotopic (as maps of pairs).

I think I know how to prove this for pairs of CW complexes. My question is just for a citable reference either in a paper or a textbook.