The Terumat Ha’deshen (Rav Yisrael Isserlin, 1390-1460) addresses the case of a Berit Mila that is supposed to take place on Purim, but one is unable to both perform the Berit and read the Megila. This can happen if neither Misva was performed until late in the day, and there is no longer enough time remaining in the day to perform both. The Terumat Ha’deshen initially suggests that in such a case one should read the Megila and perform the Berit the following day, but his conclusion is that one should fulfill the Torah obligation of Berit Mila instead of the Rabbinic obligation of Megila.
When a Berit is performed on Purim, the common custom in our community is to perform the Berit after Megila reading and the completion of Shaharit. Some have the practice of performing the Berit before Megila reading, because in the verse in the Megila, "La’yehudim Hayeta Ora Ve’simha Ve’sasson Vi’ykar," the word "Sasson" ("jubilation") alludes to the Misva of Berit Mila. Nevertheless, the practice in our community follows the view of the Kaf Ha’haim and of Hacham Ovadia Yosef (Hazon Ovadia) that the Berit should be performed after the prayer service. One reason underlying this ruling is that, as the Terumat Ha’deshen writes, the Misva of Megila is more frequent ("Tadir") than the Misva of Berit Mila, as the Megila is read each and every year, whereas Berit Mila does not occur at fixed times. Additionally, the Misva of Megila reading achieves the result of Pirsumeh Nisa – publicizing the miracle – and thus should precede the Misva of Berit Mila.
Summary: The custom in our community is that when a Berit Mila is performed on Purim, it is performed after the Megila reading and the conclusion of the morning prayer service.
