A turning tool adaptor includes opposite first and second side surfaces and a peripheral surface which extends therebetween. The turning tool adaptor further includes a cutting portion with an insert retaining portion and a clamping portion which extends from the cutting portion. The clamping portion includes a protrusion which extends transversely from the first side surface. The protrusion includes a main abutment surface and spaced apart first and second adaptor clamping bores which open out to the second side surface and also to the main abutment surface. The turning tool adaptor has first, second and third abutment surfaces which are located between the top and bottom surfaces in a side view perpendicular to one of the side surfaces.