Ruling on du‘aa’ after the Talbiyah in Hajj and ‘Umrah

The scholars are unanimously agreed that it is recommended
for the pilgrim in ihram for Hajj and ‘Umrah to recite the Talbiyah a great
deal: “Labbayka Allaahumma labbayk, labbayka laa shareeka laka labbayk.
Inna al-hamd wa’l-ni‘mata laka wa’l-mulk, laa shareeka lak (Here I am, O
Allah, here I am. Here I am, You have no partner, here I am. Verily all
praise and blessings are Yours, and all sovereignty, You have no partner).”
Then when he has finished it, he may send blessings upon the Prophet
(blessings and peace of Allah be upon him) and ask Allah for whatever he
wants, such as asking Him for Paradise and seeking refuge with Him from
Hell. 

A hadith to that effect was narrated from the Prophet
(blessings and peace of Allah be upon him), but its isnaad is da‘eef. 

Ad-Daaraqutni (2507) and al-Bayhaqi in as-Sunan al-Kubra
(5/46) narrated from Khuzaymah ibn Thaabit (may Allah be pleased with him)
that when the Prophet (blessings and peace of Allah be upon him) had
finished his Talbiyah, he would ask Allah for His good pleasure and
forgiveness, and he would seek refuge in His mercy from the Fire. 

Al-Haafiz Ibn Hajar said in Buloogh al-Maraam: Its
isnaad is da‘eef (weak). See: Talkhees al-Habeer (1005). 

Al-Qaasim ibn Muhammad ibn Abi Bakr as-Siddeeq said: It was
enjoined after completing the Talbiyah to send blessings upon the Prophet
(blessings and peace of Allah be upon him). 

Imam ash-Shaafa ‘i (may Allah have mercy on him) said: 

Rationally speaking, the one who recites the Talbiyah is
coming to Allah and his utterance of the Talbiyah reflects the fact that he
is responding to the caller who called to Allah. Part of making supplication
perfect and making it more hopeful of a response is sending blessings upon
the Prophet (blessings and peace of Allah be upon him) and asking Allah, may
He be exalted, after that, by virtue of sending blessings upon the Prophet
(blessings and peace of Allah be upon him), for Paradise and seeking refuge
with Him from Hell, for that is the greatest one may ask Him for. And after
that he may ask for whatever he wants.

End quote from Ma‘rifat as-Sunan wa’l-Athaar by al-Bayhaqi
(8/35) 

He also said: 

What I prefer is for the individual to limit the Talbiyah to
the words that were narrated from the Prophet (blessings and peace of Allah
be upon him) and not to add anything to it except what has been narrated
from the Prophet (blessings and peace of Allah be upon him), and to glorify
Allah, may He be exalted, and call upon Him after completing the Talbiyah
and pausing.

End quote from al-Umm (2/169-170) 

An-Nawawi (may Allah have mercy on him) said:

It is recommended (mustahabb), after completing the Talbiyah,
to send blessings upon the Messenger of Allah (blessings and peace of Allah
be upon him) and to ask Allah, may He be exalted, for His good pleasure and
Paradise, and to seek refuge with Him from Hell, then to offer whatever
supplication one wants.

End quote from al-Majmoo‘ (7/260) 

Ibn Qudaamah (may Allah have mercy on him) said: When the
individual has completed the Talbiyah, he should send blessings upon the
Prophet (blessings and peace of Allah be upon him) and offers supplication
for whatever he wants of good in this world and the hereafter.

End quote from al-Mughni (5/107) 

Ibn Qaasim (may Allah have mercy on him) said in his
commentary on ar-Rawd al-Murbi‘ (3/574): It is Sunnah to offer
supplication after the Talbiyah, asking for whatever one wants, and there is
no difference of scholarly opinion on that point, because this is a time
when supplication is likely to receive a response. So he should ask Allah
for Paradise and seek refuge with Him from Hell. End quote. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: The
muhrim (pilgrim in ihram) should recite the Talbiyah a great deal,
especially at changes of time and place, such as when going up or down
(whilst travelling?), or when night or day come, and after that he should
ask Allah for His good pleasure and Paradise, and seek refuge in His mercy
from Hell.

End quote from Fataawa Ibn ‘Uthaymeen (24/378) 

And Allah knows best.