Yazid issued the order to put Imam al-Husayn (as) to death

Ya‘qubi recounts, "By the time al-Husayn started off towards Iraq, Yazid had appointed ‘Ubayd Allah ibn Ziyad to be the governor of that land. Yazid wrote to his newly appointed governor, ‘News has reached me that the people of Kufah have written a letter to al-Husayn inviting him to come to them. At this very moment as I write, he is moving towards Kufah...

If you kill him, then so much the better; there will remain no more duty on you. However, if you do not put him to death, I will send you to join your dead ancestors. So beware, and do not lose this opportunity'."20

From this historical text, we can conclude that Yazid ibn Mu‘awiyah had charged ‘Ubayd Allah ibn Ziyad with the duty of killing Imam al-Husayn (as). He had even gone so far as to intimidate Ibn Ziyad with death if he dared disobey his orders.

Notes:

20. Tarikh Ya‘qubi, vol. 2, p. 242; Mukhtasar Tarikh Damishq, vol. 28, p. 19.