I tried to do so using viewport rect but once I do that I get a black screen in both cameras (depth is set for both camera correctly). Please could you point out what I might be missing?
Actually I did it using render texture. Attached an extra camera to the SteamVr camera rig and set it to that render texture and show it on UI. It is also doable through viewport rect but only if you add an extra camera and not manipulate the values inside the camera rig which was the thing I was missing.