Qunut is a supplication recited immediately before or after ruku`. It is permissible to recite the qunut aloud in any of the five daily Prayers at those times when Muslims are faced with calamities.
Sheikh Sayyed Sabiq states in his well-known book, Fiqh Us-Sunnah: It is permissible to recite the qunut aloud in any of the five daily Prayers at those times when Muslims are faced with calamities. Ibn `Abbas relates that the Messenger of Allah (peace and blessings be upon him) made qunut consecutively for one month in the Zhuhr, `Asr, Maghrib, `Isha, and Fajr Prayers. At the end of every Prayer, after saying “Allah hears him who praises Him” in the last rak`ah, he would supplicate against Ri`l, Dhakwan, and `Usiyyah of Banu Sulaim, and the people behind him would say “Ameen.” This is related by Ahmad and by Abu Dawud adding that these three tribes had killed the emissaries that the Prophet (peace and blessings be upon him) had sent to them. `Ikrimah said: “That was the beginning of the qunut.”
Abu Hurayrah reports that whenever the Prophet (peace and blessings be upon him) wanted to supplicate against or for someone, he would make qunut after going into ruku`. Sometimes, he would say “Allah hears him who praises Him. Our Lord, to You is the praise. O Allah! Save Al-Walid ibn Al-Walid and Salamah ibn Hisham and `Iyash ibn Abi Rabi`ah and the oppressed [and weak] believers. O Allah, put hardship and pressure on the tribe of Mudar and give them years of famine like those during the time of Yusuf.” He would say this aloud in some of the Prayers. Also in the Fajr Prayer, he would say, “O Allah, curse so-and-so,” cursing two tribes of Arabs until Allah revealed: “It is no concern at all of thee [Muhammad] whether He relent toward them or punish them, for they are evildoers” (Aal `Imran: 128) (This hadith is reported by Ahmad and Al-Bukhari).