Towing an Unkato supply container, I-36 got underway from Paramushiro at 10:00 on 15 June 1943 for her first supply run, with an estimated time of arrival at Kiska of 19 June. She soon lost the Unkato container in heavy seas, and while heading northeast at on 17 June 1943, she nearly ran aground on Middle Reef in the North Pacific Ocean south of Buldir Island. Concerned with an alarming rise in losses and near-losses of submarines in the Aleutians — including I-36′s near-grounding — the commander of Submarine Squadron 1 ordered the suspension of the Kiska supply effort on 21 June 1943, and I-36 turned back. She was in the Bering Sea north of Kiska an hour before dawn on 24 June 1943 when Submarine Squadron 1 ordered her to abandon her supply mission entirely and return to Paramushiro, which she reached on 25 June. I-36 and the submarine refueled from the oiler on 27 June 1943.