In [24], Koliha proved that T ∈ L(X) (X is a complex Banach space) is generalized Drazin invertible operator iff there exists an operator S commuting with T such that STS = S and σ(T2S−T) ⊂ {0} iff 0 < acc σ(T). Later, in [14, 34] the authors extended the class of generalized Drazin invertible operators and they also extended the class of pseudo-Fredholm operators introduced by Mbekhta [27] and other classes of semi-Fredholm operators. As a continuation of these works, we introduce and study the class of ɡz- invertible (resp., 1z-Kato) operators which generalizes the class of generalized Drazin invertible operators (resp., the class of generalized Kato-meromorphic operators introduced by Živković-Zlatanović and Duggal in [35]). Among other results, we prove that T is 1z-invertible iff T is 1z-Kato with p˜(T) = q˜(T) < ∞ iff there exists a commuting operator S with T such that STS = S and acc σ(T2S − T) ⊂ {0} iff 0 < acc (acc σ(T)). As application and using the concept of the Weak SVEP introduced at the end of this paper, we give new characterizations of Browder-type theorems.