The‘canonical embedding approach’ was introduced by the secondauthor and, subsequently, it has been applied several times to prove theembeddability of certain regular extensions by groups into semidirectproducts by groups. In the present paper this technique is generalizedso that it is suitable to handle regular extensions by inversesemigroups. As an application, B. Billhardt's embedding theorem onregular extensions of semilattices by inverse semigroups isreproved.