It was narrated that 'Abdullah said:

We used to talk during the prayer and greet one another with salam, and one of us would mention his need. I came to the Prophet (ﷺ) and greeted him with salam when he was praying, and he did not return my greeting. I became anxious, wondering which of my deeds might have caused this. When he finished praying, he said: “Allah, may He be glorified and exalted, introduces into His matter (religion) whatever He wills, and He has introduced (the ruling) that you should not speak during the prayer.”