A catheter-based/intravascular ablation system includes needles which expand around a central axis to engage a blood vessel or left atrium wall, allowing the injection of an ablative solution for ablating conducting tissue, or nerve fibers around the ostium of the pulmonary vein or around the renal artery. The system includes means to adjust the depth of penetration into the tissue of the targeted blood vessel wall. The catheter can include expandable guide tubes that engage the blood vessel wall. Injection needles having injection egress at or near their sharpened distal end are then advanced through the guide tubes to penetrate the blood vessel wall to a prescribed depth. The ability to provide PeriVascular injection only affecting the outer layer(s) of a blood vessel without affecting the media has particular application for PeriVascular Renal Denervation (PVRD) of the sympathetic nerves which lie in or outside the adventitia of the renal artery.