Humanity's long-term welfare may lie in the hands of those who are presently living, raising the question of whether people today hold the generations of tomorrow in their moral circles. Five studies (NTotal = 1652; Prolific) reveal present-oriented bias in the moral standing of future generations, with greater perceived moral obligation, moral concern, and prosocial intentions for proximal relative to distal future targets. Yet, present-oriented bias appears stronger for socially close compared with socially distant targets and for human targets relative to non-human animals and entities in nature. Individual differences, including longtermism beliefs and subjective imaginative vividness, predict greater concern for and obligation to the future. Likewise, concern and obligation predict greater future-oriented generosity. Our studies are among the first to explore moral considerations for targets across deep temporal expanses, reconcile conflicting evidence in the extant literature on moral judgment and future-thinking, and offer practical implications for bettering the shared societal future.