  For a large class of hierarchies of integrable equations admitting a
classical $r-$matrix, we propose a construction for the Virasoro algebra
actionon the Lax operators which commutes with the hierarchy flows. The
construction relies on the existence of dressing transformations associated to
the $r$-matrix and does not involve the notion of a tau function. The
dressing-operator form of the Virasoro action gives the corresponding
formulation of the Virasoro constraints on hierarchies of the $r-$matrix type.
We apply the general construction to several examples which include KP, Toda
and generalized KdV hierarchies, the latter both in scalar and the
Drinfeld-Sokolov formalisms. We prove the consistency of Virasoro action on the
scalar and matrix (Drinfeld-Sokolov) Lax operators, and make an observation on
the difference in the form of string equations in the two formalisms.
