Among the people - The Israelites.
Among the nations - The Gentiles at large. A prophecy either relating to the Gospel times, Christ being considered as the Speaker: or a prediction that these Divine compositions should be sung, both in synagogues and in Christian churches, in all the nations of the earth. And it is so: wherever the name of Christ is known, there is David's known also.
I will praise thee, O Lord, among the people - So great a deliverance as he here hoped for, would make it proper that he should celebrate the praise of God in the most public manner; that he should make his goodness known as far as possible among the nations. See the notes at Psalm 18:49.