Abstract: w-E-pure exact sequences and absolutely w-E-pure modules are introduced and studied. We obtain that the class of absolutely w-E-pure modules are closed under w-E-pure submodules and extensions, respectively. It indicates that in some sense absolutely w-E-pure modules can be seen as the dual of w-copure flat modules. Finally, w-IFrings are characterized in terms of absolutely a w-E-pure modules.