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.