Is it permissible to delay prayer in order to solve problems?

Praise
be to Allah

If a Muslim is
trying to bring about reconciliation between two people or two groups, and
the time for prayer comes, and he fears that if he goes to pray the people
may disperse without reconciliation being achieved, then there is no blame
on him if he delays offering prayer in congregation with the first
congregation, then prays in congregation after that, or by himself if he is
not able to pray in congregation. That is a valid excuse for not offering
the prayer in congregation or delaying it.

Al-Bukhaari
(2690) and Muslim (421) narrated from Sahl ibn Sa‘d (may Allah be pleased
with him) that there was a dispute among some people from Banu ‘Amr ibn
‘Awf, so the Messenger of Allah (blessings and peace of Allah be upon him)
went out to them, with some of his companions, to bring about reconciliation
among them. The time for prayer came, but the Prophet (blessings and peace
of Allah be upon him) did not come [to the mosque]. Bilaal came and gave the
call to prayer, but the Prophet (blessings and peace of Allah be upon him)
did not come. So Bilaal went to Abu Bakr and said: The Prophet (blessings
and peace of Allah be upon him) has been detained (by some matter) and it is
time to pray; will you come and lead the people in prayer? He said: Yes, if
you wish. So he gave the iqaamah (the call immediately preceding the
prayer), and Abu Bakr went forward (to lead the people in prayer) …

If the prayer is
one that can be joined to the prayer that comes after it, such as Zuhr,
which may be joined with ‘Asr, or Maghrib, which may be joined with ‘Isha’,
then it may be joined with the later prayer, and there is nothing wrong with
delaying it and praying the two prayers together.

The Sunnah
indicates that it is permissible to put two prayers together if there is an
excuse for doing so, even if one is at home and not travelling.

Ibn Rajab al-Hanbali
(may Allah have mercy on him) said:

Ahmad stated
that it is permissible to put two prayers together in the event of being
engaged in some pressing business.

It was narrated
from Ibn Sireen: There is nothing wrong with putting two prayers together
when there is a need to do so, so long as that is not taken as a habit. End
quote.

Fath al-Baari
by Ibn Rajab (3/93)

As for delaying
prayer until its time has ended without putting it together with the
following prayer, if the two prayers can be put together, that is not
permissible.

Rather what
should be done is to offer the prayer on time; in this case the person may
forego praying in congregation in the mosque, and offer the prayer with
those whom he is seeking to reconcile, to ensure that the meeting will not
end before the people have been reconciled.

And Allah knows
best.