I can't tell if the pot texture is porous, but I would try--don't laugh--using a whitening toothpaste on it first, using an old toothbrush, starting out with a stiff bristle brush. Then, if that doesn't work, a product like CLR, which removes calcium, lime and rust stains.
I agree with Ellis. If the surface of your planter is porous, you may have limited success in removing the built-up mineral stains. You can also try using clear vinegar and salt mixed to a paste, scrub with a toothbrush to see if you can dissolve the mineral build-up.
CLR and stiff brush just so you don't tear up planter then rinse/dilute really well so it doesn't leach up into plant roots I use it on all of mine if it's still present try some Iron Out
We've used this stuff
on everything (boats, floors, seats, etc.) to remove water spots, mold, anything that's difficult to get off with a normal cleaner.
Spray it on and just watch it go back to it's normal color and then wipe it off. This stuff is amazing!
Spray on some bleach. Works wonders, breaks down in light. Brush with a stiff bristle brush