Charles Ellicott Commentary Esther 9:31

"to confirm these days of Purim in their appointed times, according as Mordecai the Jew and Esther the queen had enjoined them, and as they had ordained for themselves and for their seed, in the matter of the fastings and their cry." — Esther 9:31 (ASV)

To confirm ... enjoined ... decreed. — The same Hebrew verb stands for the three different English verbs; it is also the word stablish in Esther 9:21. To fix or settle represents the meaning.

The matters of the fastings and their cry. — These words appear rather awkwardly. For this reason, and also because they are omitted by the Septuagint, some have doubted their genuineness here. All Hebrew manuscripts, however, and all the other ancient versions, retain the words. We must, therefore, suppose that the Jews throughout the empire had instituted fasts and lamentations, in addition to what Mordecai’s letter had prescribed. Thus, we may probably connect this with the fast now observed on Adar 13.