A new and distinct cultivar of Rose plant named `Pejamblu` is characterized in compact upright bush having a mauve/lilac color flowers ageing to a slate blue and having a strong pleasant fragrance. The plant also benefits from a lengthy flowering period of repeated flowerings between spring and fall. The plant is tolerant of dry conditions and exhibits tolerance to Black Spot and Powdery mildew, Rust mildew, and Downey mildew.