Can you cast spells during the untap step?

During the untap step, no player receives priority at all. Priority is the permission system that lets players cast spells and activate abilities, so without it, neither player can do anything except watch the game's automatic untap actions resolve. This is stated explicitly in Comprehensive Rule 502.3.

CR 502.1 defines the untap step as the first step of the beginning phase. CR 502.3 states directly: 'No player receives priority during the untap step, so no spells can be cast and no abilities can be activated.' This makes it one of only two steps (along with the cleanup step, under normal circumstances) where players simply cannot act.

The untap actions themselves are not spells or abilities — they are simply a game action the active player performs (or the game performs automatically under CR 502.2), so they cannot be responded to either.

Concrete example: Your opponent controls a creature with a tap-activated ability. You might hope to activate it 'in response to untapping,' but you cannot — the untap step ends and moves directly to the upkeep step before anyone gets priority. You would have to wait until the upkeep step (or later) to act.

If you need to do something 'before untap,' the closest option is during your opponent's end step on their previous turn, which is the last time priority is passed before the untap step begins.