By a coprime commutator in a profinite group G we mean any element of the form [x, y], where \(x,y\in G\) and \((|x|,|y|)=1\) . It is well-known that the subgroup generated by the coprime commutators of G is precisely the pronilpotent residual \(\gamma _\infty (G)\) . There are several recent works showing that finiteness conditions on the set of coprime commutators have strong impact on the properties of \(\gamma _\infty (G)\) and, more generally, on the structure of G. In this paper we show that if the set of coprime commutators of a profinite group G is covered by countably many procyclic subgroups, then \(\gamma _\infty (G)\) is finite-by-procyclic. In particular, it follows that G is finite-by-pronilpotent-by-abelian.
