What should I say when the call is made for the obligatory congregational prayer to begin in the mosque, and is this an occasion for invoking blessings upon the Noble Messenger, may God's prayers and peace be upon him?

There are two issues regarding praying upon the Prophet, peace and blessings of Allah be upon him, during the Adhan and Iqamah:

The First Issue: Is it recommended to pray upon the Prophet, peace and blessings of Allah be upon him, before the Iqamah? The correct view is that it is not recommended, because there is no evidence for it from the Prophet, peace and blessings of Allah be upon him, nor from his Companions. Rather, it is closer to being an innovation (bid'ah). Indeed, the verifying scholars among the Shafi'is have denounced this.

The Second Issue: Is it recommended for the person calling the Iqamah and those who hear the Iqamah to pray upon the Prophet, peace and blessings of Allah be upon him, after finishing it? The majority of scholars are of the view that it is recommended, based on the hadith: "When you hear the Mu'adhdhin, then say as he says, then send prayers upon me." This includes both the Adhan and the Iqamah. This has been reported in the statements of some Companions and Tabi'un. Others are of the view that it is not recommended to respond to the person calling the Iqamah, and that the hadith reported concerning this is weak.