An intravascular catheter for peri-vascular or peri-urethral tissue ablation includes multiple needles advanced through supported guide tubes which expand with open ends around a central axis to engage the interior surface of the wall of the renal artery or other vessel of a human body allowing the injection an ablative fluid for ablating tissue, such as nerve fibers in the outer layer or deep to the outer layer of the vessel, or in prostatic tissue. The system also controls the depth of penetration of the ablative fluid into and beyond the tissue of the vessel wall. The catheter includes structures which provide radial and lateral support to the guide tubes so that the guide tubes open uniformly and maintain their position against the interior surface of the vessel wall as the sharpened injection needles are advanced to penetrate into the vessel wall.