Why were the chieftains of Edom and the strong men of Mo'av afraid?
Rashi: Even though they knew that Yisrael were not threatening them (Mechilta 1 ), they were pained over the honor of Yisrael.
Ramban (citing Ibn Ezra) 2 : If not for the fear of Hashem, they would have attacked Yisrael out of hatred. Mo'av includes Amon.
Seforno: They were simply overawed by the magnitude of the miracles.
Refer to 15:14:2:2.
Sifsei Chachamim: The command not to attack them was already given even though it was not written until later (Devarim 2:5,9). (Who told this to Edom and Mo'av? The Mechilta says that even though we could not take their land, they feared lest we return the hatred or feud between their ancestors and ours. - PF)