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Hajj Chant "Labaayk" to be recited for the duration of the time one is in Ihram
"Ever at Your service, O Allah, every at Your service. Ever at Your Service, You have no partner, ever at Your service. Verily all praise, blessings and dominions are Yours. You have no partner" (repeat three times)
Supplication upon first seeing the Ka'bah
"O Allah, increase this house in nobility, honour, reverence, and dignity. Increase those going on Hajj or Umra, who honour and revere it, in honour, reverence and piety. O Allah You are Peace, the source of Peace; O Lord raise us after death in peace." Then one asks Allah for whatever one wishes of religious matters or those of this world.
General Dua to be recited during the circumambulation of the Ka'bah
"Glory be to God, and praise be to God! There is no deity save God. God is Supreme. There is no strength or power save in God."
"O Allah, make this a pious Hajj, a rewarded effort, and forgive my sins"
"My Lord, forgive me, show me mercy, and Pardon that which You know. Verily You are the All-Powerful and the Most Generous. Our Lord, give us what is good in this world and the next, and keep us from the tormet of hell."
Supplication when kissing the Black Stone
"O Allah, out of faith in You and to affirm Your book, fulfill Your covenant, and follow the sunnah of Your Prophet Muhammad (PBUH)"
To be recited between the Black Stone and the Maqam Ibrahim
"O God! Cause me to be content with that wherewith Thou providest me, and bless me therein, and represent me well in all my affairs in my absence."
When passing the Ka'bah door in circumambulation whilst heading towards the Maqam Ibrahim
"O Allah, verily this is Your house, the sanctuary Your sanctuary, the safety Your safety, and this is the station of him who took refuge in You from fire"
When passing the corney by Hijr Ismail
"O Allah I take refuge in You from doubt, from ascribing partners to You, from discord, hypocrisy, evil traits, and from bad turns of fortune in money, spouse, and children."
When passing the rainspout at the top of the Ka'bah
"O Allah, shade me in Your shade on a day when there is no shade but Yours. Give me to drink from the cup of Your Prophet Muhammad (PBUH), a wholesome drink after which I will never thrist."
When passing the Yamani corner
'O God! Behold, I beg of Thee forgiveness and safety in this world and the Hereafter. Our Lord! Bestow upon us the good in this world, and the good in the Hereafter, and save us from the torment of the Fire.'they (the angels) say 'Amen.'"
(Abu Hurayrah - Ibn Majah)
To be recited between the Yamani corner and the third corner
"O Allah, make this a pious Hajj, a rewarded effort, an accepted work, and a transaction that will never perish, O All-Powerful and Oft-forgiving One"
To be recited after tawaf behind the Maqam Ibrahim
"O Allah, this is Your city, and al-Masjid al-Haram, and Your inviolable house, and I am Your slave, the son of Your slave and bondwoman. I have come to You with many sins, mistakes, and wicked acts, and this is the station of him who took refuge in You from the fire; so forgive me, verily You are the All-forgiving and Compassionate. O Allah, You have called Your servants to Your inviolable house, and I have come, asking for Your mercy and seeking Your pleasure, You are the Rewarder, so forgive me and have mercy on me, verily You have power over everything."
After having offered two rakahs, Prophet Adam (AS) prayed behind the Maqam Ibrahim:
"O God! You know that which is secret and that which is manifest in me; so accept my apology, You are aware of my need; so grant my petition. You know that which is in my mind, so forgive me my sins. O God I beg of You a faith which will engage my heart in firm conviction, so that I may realise that nothing will befall me save what You have prescribed for me, a feeling of satisfaction with that You have alloted unto me. O Thou Most merciful of those who show mercy!"
Whereupon God the Most High revealed Himself unto him saying: 'O Adam! Thy request unto Me was such that it has to be granted. I have pardoned thy sins, and solved all thine anxieties and griefs. None of thy progeny after thee shall recite this prayer but I will deal with him likewise. I will make his trade prosper more than the trade of any trader, and the world shall attend on him, though he be averse thereto.'
To be recited on drawing near to al-Safa
"'Behold al-Safa and al-Marwah are among the Indications of God.' I begin wherewith God began."
To be recited on al-Safa facing the Ka'ba
"There is no deity save God. He is Alone. God is Supreme. There is no deity save God. He is Alone. He Hath no partner. Unto Him belong the sovereignty, and unto Him belong the praise; and He is All-Powerful. There is no deity save God. He is alone. He fulfilled His promise, helped His bondman, and alone routed the Confederates. There is no deity save God. We worship none but Him, making our religion sincerely for Him, though unbelievers be averse." (Repeat three times)
Then it is advised to supplicate for whatever one wishes as it is one of the places where prayers are answered.
To be recited between Safa and Marwa
"My Lord, forgive, show mercy, and overlook that which You know. Verily You are the Most Powerful and Generous. O Allah, our Lord, give us what is good in this world and the next, and protect us from the torment of hell."
To be recited on the way to Arafa
"O Allah to You I betake myself, seeking Your noble countenance. Forgive me my sins, make my hajj a pious one, show me mercy, and do not disappoint me"
When standing at Arafa
It is recommended to stand exposed to the sun facing the direction of prayer (qibla) with ones heart fully attentive and not occupied with wordly matters, and to do much chanting of "Labbayk," reciting blessings on the Prophet (PBUH), asking Allah's forgiveness, supplicating and weeping, for here tears are shed and mistakes annulled. The greater parts of one's words should be:
"There is no deity save God alone, without partner. His is the dominion, His the praise, and He has power over everything."
And one should pray for one's family, friends and all Muslims.
When stopping at al-Mash'ar al-Haram in Muzdelifa
"O Allah, as You have brought us to stand in it and shown
us to it, so too, give us success in Your remembrance, as You have guided us.
Forgive us, and show us the mercy You have promised us by saying (and Your word
is the truth):
When released from Ihram: after one's hair has been cut
"O Allah, for each hair reckon for me a good deed, annul a bad one, and raise me a degree. Forgive me, those who shave their hair, those who shorten it, and all the Muslims."
After the farewell circumambulation (tawaf)
After the farewell circumambulation, one prays two rak'as and stands at the place between the Black Stone and the door of the Ka'aba, and supplicates:
"O Allah, the House is Your House, the servant Your servant and son of Your two servants. You have carried me on a creature You have made submissive to me, bringing me to Your city and showing me Your grace that I might fulfill Your rites. If You are pleased with me then be the more so, and if not, then bless me now before my residence and the place where I am visited grow far from Your House. Now is the time I depart if You permit me, who seek none but You and no other than Your house, and am not averse to You or Your house. O Allah, give me good health in body and protect me in my religion. Make my affairs turn out well and give me the sustenance of obedience to You as long as You let me live. Give me the best of this world and the next, for truly, You have power over everything."
For various downloadable Hajj Duas click here
(Source: Prayers of Muhammad, Sh. Muhammad Ashraf; Reliance of the Traveller, Ahmad ibn Naqib al-Misri (translated by Noah Keller)