Esther 3-4: Haman is offended by Mordecai's lack of respect and schemes for the Jews' destruction.

Haman (a descendent of King Agag, an Amalekite) is raised to power in Persia, and he becomes offended and angered when Mordecai refuses to bow and give honor.
This is not because of a religious prohibition against bowing, but rather refusing to bow to an Amalekite.
We have an interesting situation in that, if King Saul, 600 years earlier, had obeyed God and removed the remaining Amalekites -- there would be no Haman.
And if King David had NOT shown mercy to Shimei, a member of Saul's family (in 2nd Samuel 16), there would have been no Mordecai.
Haman vows to annihilate all of the Jews in Persia (which include those back in Israel, now a Persian province. Before presenting his plan to King Xerxes, Haman uses is own brand of divination to determine the best date to carry out this genocide. (Which, by God's providence is almost a year later.) this casting of lots (called 'pur') is the basis for the feast name of "Purim" which celebrates God's deliverance.
Through lies and bribery, Haman gets the Kings approval, and the date is set by law for the Jews' extermination.
Mordecai discovers this new edict, and approaches Queen Esther, pointing out that, if this decree is carried out, she too will be among the dead. At this time, no one knows that she is Jewish.
Queen Esther asks that Mordecai gather Jews together for fasting. (Neither God nor prayer is mentioned in the book of Esther.
She declares that, after the time of fasting, she will risk her life and enter the king's presence without invitation.