Atos 2:39

The "promise" is the gift of the Holy Spirit (Acts 1:5; Acts 1:8; Acts 2:33). Those "far off" probably include the Diaspora Jews, future generations of Jews, and the Gentiles. Peter had already expressed his belief that Gentiles could be saved (Acts 2:21; cf. Joel 2:32), a fact taught repeatedly in both the Old and the New Testament. Peter’s later problem involving the salvation of Cornelius was not due to a conviction that Gentiles were unsaveable. It was a question of the manner by which they became Christians (i.e., not through Judaism, but directly without becoming Jews first). Note, too, Peter’s firm belief in God’s sovereignty (cf. Acts 2:23). God takes the initiative in calling the elect to salvation, and then they repent (Acts 2:38; cf. John 6:37; Romans 8:28-30).