Exhibit 99.1 For Immediate Release — 7:01 am ET on Wednesday, May 15, 2024 Acurx Pharmaceuticals, Inc. Reports First Quarter 2024 Results and Provides Business Update Staten Island, NY, May 15, 2024 — Acurx Pharmaceuticals, Inc. (NASDAQ: ACXP) (“we” or “Acurx” or the “Company”), a clinical stage biopharmaceutical company developing a new class of antibiotics for difficult-to-treat bacterial infections, announced today certain financial and operational results for the first quarter ended March 31, 2024. High ...