The best fix is to stop water from sitting between the planter and the tiles. Rust stains usually happen because moisture, condensation, or runoff keeps the metal base wet for long periods. Start by lifting the planter off the balcony surface. Use plastic or rubber planter risers, a sturdy drip tray, or a waterproof saucer under the box. Avoid direct metal-to-tile contact, because even a coated base can scratch and begin to rust over time.
If your planter is metal, check the inside for rusted seams, screws, or drainage hardware. Clean away loose rust, then seal the metal with a rust-inhibiting paint or use a plastic liner as a barrier between the soil and the metal. Make sure the liner still allows drainage, and empty any drip tray regularly so water does not collect underneath. Also keep the planter slightly away from the wall and ensure its drainage holes flow onto a tray or safe surface, not directly onto the tiles.
For existing rust marks, test a small hidden area first. For many glazed ceramic or porcelain tiles, a paste of baking soda and a little water, followed by white vinegar, can help with light marks. For tougher stains, use a commercial rust remover or oxalic acid product that is safe for your tile type, and follow the label carefully. Avoid steel wool and harsh acids on natural stone, and rinse thoroughly afterward. Once the tiles are clean and dry, keep the planter elevated, use a waterproof liner, and check underneath after rain to prevent the stains from coming back.