Use "Mesh > Sweep > Element", this command is really powerful and you can mesh with HEX elements instead TET.
Also take a look to this post: https://iberisa.wordpress.com/2011/10/16/mallado-con-elementos-hexaedricos-hex-meshing-iii/
Thanks for the detailed response. I try to use Hexa mesh all the time. But there are more complex cases where tetra meshing would be preferable and hexa-sweeping is expensive terms of time.
You always can mesh previously ALL surfaces of the solid with PLOT PLANAR 2-D "SEED MESH" and use NEXT regular command "Mesh > Geometry > Solids" as ever, this gives you freedom to mesh any solid with TET elements after meshing locally any surface (face) of the solid with a 2-D quality mesh using any option of the "MESH > MESH CONTROL > APPROACH ON SURFACE" command.
The TET mesher will "honor" all the 2-D Seed mesh based in PLOT PLANAR elements.