In the Friday Khutbah should we raise our hands during the Du'a?
Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Neither the Imam nor the Muslims who are praying with him should raise their hands during the Khutba (Friday sermon) except during Istisqa (Du'a supplication for rain). In this case it is even a Sunnah for them to do so. On the other hand, the scholars have divided raising hands during Du'a into three situations.
First, if it is proved that the Prophet raised his hands during a given Du'a, in this case it is a Sunnah to do so like during the Istisqa Du'a (supplication to have rain).
Second, if it is proved that the Prophet made a certain Du'a and did not raise his hands, like his Du'a during Friday Khutba except while making Istisqa, and his Du'a between the two prostrations and before the Taslim, it is not recommended by the Shariah to raise hands during these situations as the Prophet's deed is an evidence to do something and his avoidance to do something is also a proof that thing is not to be done.
The third situation is all types of Du'a which do not fit into one of the above categories. In this case it is from Sharia that the person raises his hands for the Ahadith that urge doing so and which state that raising hands in Du'a is a cause for having ones Du'a answered positively. The Prophet said: "Your Lord is munificent and generous, and is ashamed to turn away empty the hands of His servant when he raises them to Him".(Abu Dawood and Tirmizi).
Allah knows best.
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