The context of the Numbers passage is Balak's attempt to have Balaam curse Israel into oblivion out of malice. Numbers 23:19 is God's affirmation of constancy - that He will not arbitrarily let Israel be destroyed. The fuller translation of Balaam's words (JPS Tanakh) is:
19 God is not man to be capricious, Or mortal to change His mind.
Would He speak and not act, Promise and not fulfill?
20 My message was to bless: When He blesses, I cannot reverse it.
The context of the Deuteronomy passage is entirely different. In this case, Israel had turned from God to idol worship during the very time that God was giving his word to Moses on Mt. Sinai (v.1-6). God's request to Let Me be (v.10) has been interpreted by both Jewish and Christian commentators to be a hint for Moses to pray for deliverance from God's just punishment. Rashi (1040-1105), for example, comments:
But here, He opened a door for him and informed him that the matter
indeed depended upon him Moses, that if he Moses would pray for them,
He God would not destroy them.1
The same interpretation is given in Christian commentaries of Ephrem the Syrian (306-373), Jerome2 (347-420), and Augustine3 (354-430). Ephrem recalls Moses' prayer in the context of Jesus' parable of the barren fig tree (Luke 13:6-9):
When he wished that the fig tree be uprooted, the event was similar to
that earlier one, when the Father said to Moses, “Permit me to destroy
the people.” He thus gave him a reason to intercede with him. Here too
he showed the vinedresser that he wished to uproot it. The vinedresser
made known his plea, and the merciful one showed his pity, that if, in
a further year, the fig tree did not yield fruit, it would be
Thus, whereas the Numbers passage affirms God's faithfulness towards Israel, the Deuteronomy passage shows that this faithfulness can persist even when Israel itself turns from God through the intercessory prayer of those who remain faithful.
1 Commentary on the Diatessaron of Tatian 14.27
2 e.g. Homily on Psalm 26
3 e.g. Sermon LXXXVIII