Berakhot 30b:14ברכות ל׳ ב:י״ד
MISHNA: One may only stand and begin to pray from an approach of gravity and submission. There is a tradition that the early generations of pious men would wait one hour, in order to reach the solemn frame of mind appropriate for prayer, and then pray, so that they would focus their hearts toward their Father in Heaven. Standing in prayer is standing before God and, as such, even if the king greets him, he should not respond to him; and even if a snake is wrapped on his heel, he should not interrupt his prayer.
Berakhot 32b:26ברכות ל״ב ב:כ״ו
Additionally, we learned in the mishna: Even if the king greets him while he is praying, he should not respond to him as one may not interrupt his prayer.
Shulchan Arukh, Orach Chayim 104:1שולחן ערוך, אורח חיים ק״ד:א׳
To Not Interrupt In The [Middle Of The Amidah] Prayer. Containing 8 S'ifim: One may not interrupt during one's prayer [i.e. Amidah]. And even if a Jewish king is inquiring about one's well-being, one may not respond to him. But [regarding responding to] a king of the nations of the world, if one is able to shorten [one's prayer], meaning that one would say the beginning of the blessing and its end before the [king] reaches one, one should shorten it. Or if [one's on the road and] one is able to veer off the road, [then] one should veer off, but one may not interrupt by talking. And if it's impossible for one [to do so], one may interrupt.
Mishnah Berurah 104:1משנה ברורה ק״ד:א׳
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Arukh HaShulchan, Orach Chaim 104:1ערוך השולחן, אורח חיים ק״ד:א׳
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Jerusalem Talmud Berakhot 5:1:22תלמוד ירושלמי ברכות ה׳:א׳:כ״ב
They said about Rebbi Ḥanina ben Dosa that he was standing in prayer when a brightly dotted snake came and bit him. He did not interrupt his prayer. They went and found that dotted snake lying dead at the entrance of its hole. They said, woe to the human who is bitten by a dotted snake, but woe to the dotted snake that bites Rebbi Ḥanina ben Dosa. [What is the nature of that dotted snake? If it bites a human and the human reaches water first, the dotted snake dies, but if the dotted snake reaches water first, the human dies.] His students asked him: Rabbi, did you not notice? He said to them: There should happen to me these things; I was concentrating on my prayer and did not notice! Rebbi Isaac ben Eleazar said, the Holy One, praise to Him, created a well under his foot soles, to confirm what has been said (Ps. 145: 19): “He will do the will of those who fear Him, He will hear their entreaties and save them.”