Punishment serves as a balancing force that dissuades people from acting selfishly, which complements cooperation as an essential characteristic for the prosperity of human societies. Past studies using economic games with two options (cooperation and defection) reported that cooperation decisions are generally faster than defection decisions and that time pressure possibly induces human players to be more intuitive and thus cooperative. However, it is unclear where punishment decisions sit on this time spectrum. Therefore, we recruited human players and implemented two series of online network games with cooperation, defection, and punishment options. First, we find that punishment decisions are slower than cooperation or defection decisions across both game series. Second, we find that imposing experimental time pressure on in-game decisions neither reduces nor increases the frequency of punishment decisions, suggesting that time pressure may not directly interact with the mechanisms that drive players to choose to punish.