Throughout this paper we assume that every ring has unity and all modules are unital right modules. A ring R is called a (right) q-ring if every right ideal of R is quasi-injective , In this paper we study a generalization of this concept. A ring R is called a (right) weak q-ring (in short, wq-ring) if every right ideal of R, not isomorphic to RR, is quasi-injective. A ring R is called a right pq-ring if every proper right ideal of R is quasi-injective. Any upper triangular 2 X 2 matrix ring over a division ring is a wq-ring, which is not a q-ring. In Section 1, some general properties of wq-rings are established and, in particular, it is shown in (1.8) that a semiprime wq-ring has zero singular ideal.