A Brit Milah should be performed on the infant's eighth day (including the day of birth), after sunrise. If the circumcision was performed before sunrise on the eighth day, it is nevertheless valid, so long as it took place after daybreak.
Many people are unfortunately unaware of the Halacha that a circumcision should be performed specifically early in the day, due to the principle of "Zerizin Makdimin Le'mitzvot" – those who are zealous in Mitzva observance perform the Mitzvot early, without delay. One should not delay a circumcision until the afternoon, or even until the late morning hours. The Levush (Rabbi Mordechai Yaffe, Prague, 1530-1612) writes that so long as one performs the Brit Milah before the fifth hour of the day, he has fulfilled the requirement of "Zerizin Makdimin."
The Chida (Rabbi Chayim Yosef David Azulai, Israel-Italy, 1724-1806) addresses the question of whether or not the rule of "Zerizin Makdimin" overrides the principle of "Be'rov Am Hadrat Melech," that Mitzvot should be performed in the presence of large crowds of Jews. Meaning, should one delay a Brit Milah so that more guests will be able to attend the ritual? The Chida concludes that the concern for Zerizut, for alacrity in Mitzva observance, supersedes the value of a large crowd, and he therefore rules that a Brit Milah should not be delayed for guests. This is also the ruling of Rabbi Chayim Palachi (Rabbi of Izmir, Turkey, 19th century).
When a circumcision is performed on a fast day, many people have the custom to perform the Brit Milah late in the day, so that the meal – which is conducted after the fast – will occur immediately after the circumcision. However, Chacham Ovadia Yosef ruled that this is incorrect. Even on fast days, one should conduct the Brit Milah early in the morning, despite the fact that the meal is held only much later, after the fast.
Numerous sources emphasize the importance of performing a Brit Milah early in the day. The Sedei Chemed (Rabbi Chayim Chizkiya Halevi, Turkey-Israel, 1832-1904 – Ma'arechet Zayin, 3; listen to audio for precise citation) denounces the practice among some people to delay the Brit Milah to the afternoon or late morning hours, emphasizing that there is no Halachic basis for doing so. Likewise, the Or Zarua (Rabbi Yitzchak of Vienna, 1180-1250) remarks that one who delays the Mitzva of circumcision demonstrates his contempt for this Mitzva. In fact, one of the Kabbalists commented that the reason why so many Jews today – particularly youngsters – are lazy by nature is perhaps because their very first Mitzva – Brit Milah – was delayed. The slothful attitude that accompanied their initial entry into the world of Mitzvot may have affected their personalities to such an extent that they became lazy by nature.
Summary: It is critically important that a Brit Milah be performed early on the eighth day, before the fifth hour of the day. One should not delay a Brit Milah even to allow for greater attendance. Even on a fast day, when the festive meal is held at night, after the fast, the circumcision itself should nevertheless take place early in the morning.