1. leaving no opportunity for denial or refusal; imperative: a peremptory command.
2. imperious or dictatorial.
3. positive or assertive in speech, tone, manner, etc.
a. that precludes or does not admit of debate, question, etc.: a peremptory edict.
b. decisive or final.
c. in which a command is absolute and unconditional: a peremptory writ.
The person was such a shame to the town that the mayor told him in a peremptory tone that he had to leave and never come back.