The covenant is the Abrahamic covenant — the covenant God made with Abraham.
In Acts 3:25 Peter tells Israel, "Ye are the children of the prophets, and of the covenant which God made with our fathers, saying unto Abraham, And in thy seed shall all the kindreds of the earth be blessed." Les Feldick emphasizes that this is the Abrahamic covenant, that the promised Seed is the Christ, and that God planned through Israel to bring blessing to all the world.
Acts 3:25 — Peter explicitly identifies the covenant as one God made with the fathers, saying to Abraham, 'In thy seed shall all the kindreds of the earth be blessed.'
Genesis 3:15 — Les traces the 'seed' of the Abrahamic covenant back to the seed of the woman, which he identifies as the Christ.
Genesis 12:3 — This is the original covenant promise to Abraham that Peter's words in Acts 3:25 echo.
The verse itself supplies the answer. In Acts 3:25, Peter says to his Jewish audience, "Ye are the children of the prophets, and of the covenant which God made with our fathers, saying unto Abraham, And in thy seed shall all the kindreds of the earth be blessed." The covenant is therefore the one God made with Abraham: a covenant promising that Abraham's seed would bring blessing to every family and kindred on earth. The preceding verse also connects this to prophecy: "Yea, and all the prophets from Samuel and those that follow after, as many as have spoken, have likewise foretold of these days." The Bible itself does not use the label "Abrahamic covenant" in this verse, but it clearly describes the covenant God made with the fathers and then says it was spoken unto Abraham.
Les Feldick explains that in Acts 3:25 Peter is identifying the Abrahamic covenant. He repeatedly says Peter is "still on covenant ground" when addressing the nation of Israel shortly after Pentecost. Les ties the phrase "in thy seed" back to Genesis 3:15, the seed of the woman, and says that Seed is the Christ. For Les, the Abrahamic covenant is "the bedrock of everything that God has been doing in order to redeem mankind." Les also notes that the same covenant was repeated to Isaac and Jacob, and that God's blessing was for all the world but had to come through Israel. Peter, as a Jew himself, says to the nation, "You are the children of the covenant" and "You're the covenant people." Peter's message on covenant ground includes "unto you first" — Israel first — and Les lists the Abrahamic, Davidic, Palestinian, and Mosaic covenants as part of that covenant ground.
Les emphasizes that Peter, in Acts 2 and Acts 3, is speaking to the nation of Israel and is on covenant ground. Everything through the Gospels was the fulfilling of "the covenant which God made with Abraham." Peter claims the covenant promises out of Genesis, saying, "the God of Abraham, and of Isaac, and of Jacob, the God of our fathers" has glorified His Son Jesus.
Les rehearses the covenant: "I will make of you a great nation, your name shall be great. And then the end of that covenant was that through this man salvation would go to the ends of the earth." He adds that God repeated it to Isaac and to Jacob. Peter quotes the heart of it: "in thy seed shall all the kindreds of the earth be blessed."
Les says that in the seed of Abraham we can also go all the way back to Genesis 3:15, the seed of the woman. "Who was the seed of the woman? Who was the seed of Abraham? Well, the Christ." Thus the covenant is tied to God's plan of redemption for the whole human race through Israel.
Acts 3:25 says "all the kindreds of the earth" are blessed in Abraham's seed. Les explains it this way: "It was for all the world, but it had to come through Israel." The blessing was not separate from Israel; Israel was the God-appointed channel. Peter therefore says to the Jews, "You are the children of the covenant," and "unto you first" God sent His Son to bless.
Covenant Fulfilled in Acts 2
Les points out that Peter is speaking to the house of Israel, not Gentiles, and that everything through the Gospels was fulfilling the covenant God made with Abraham.
The Seed of Abraham Is Christ
Les explains that 'children of the covenant' refers to the Abrahamic covenant and that 'thy seed' goes back to Genesis 3:15, the seed of the woman — the Christ.
Children of the Covenant
Les stresses the plain language of Acts 3:25 and that this covenant began with Abraham; then 'unto you first' directs the promise to Israel.
Abrahamic Covenant Is the Bedrock
Les says Peter is on covenant ground and that the Abrahamic covenant is the bedrock of everything God has been doing to redeem mankind.
The Promise Repeated to Isaac and Jacob
Les shows that God made the same covenant promise to Abraham, Isaac, and Jacob, and that Peter is claiming those covenant promises in Acts 3.
Covenant Ground Includes All the Covenants
Les lists the Abrahamic, Davidic, Palestinian, and Mosaic covenants and notes Peter's word 'unto you first' to the nation of Israel.
All the World Blessed Through Israel
Les explains that the Messianic blessing was for all the world, but it had to come through Israel.
Peter Claims Only the Abrahamic Promises
Les shows that in Acts 3:25 Peter is claiming nothing more than the promises of the Abrahamic covenant.
Acts 3:25: Ye are the children of the prophets, and of the covenant which God made with our fathers, saying unto Abraham, And in thy seed shall all the kindreds of the earth be blessed.
This is the central verse that names the covenant and its promise to Abraham.
Acts 3:24: Yea, and all the prophets from Samuel and those that follow after, as many as have spoken, have likewise foretold of these days.
Shows the prophetic background for the covenant and for Peter's message to Israel.
Acts 3:26: Unto you first God, having raised up his Son Jesus, sent him to bless you, in turning away every one of you from his iniquities.
Shows that the covenantal blessing was sent first to Israel.
Genesis 3:15: And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel.
The seed promise that Les traces forward to Abraham's seed, the Christ.
Genesis 12:3: And I will bless them that bless thee, and curse him that curseth thee: and in thee shall all families of the earth be blessed.
The heart of the Abrahamic covenant that Acts 3:25 repeats.
It is the covenant God made with Abraham. Peter says the Jewish people are children of the prophets and of this covenant, in which Abraham's seed would bring blessing to all kindreds of the earth.
Peter says the Jewish people are the children of the covenant. Les Feldick explains that Peter is telling the nation of Israel, "You're the covenant people."
Les says that the seed of Abraham goes all the way back to Genesis 3:15, the seed of the woman, and that this seed is the Christ.
Because the covenant promises and the risen Son were sent first to Israel. Les says Peter is resting on covenant ground and telling the nation of Israel, "Unto you first."
Watch the Teaching: What Shall We Do? Acts 2 & God's Foreknowledge Explained