The New Testament writers recognized their own writings as Scripture. Paul, in II Corinthians 3:5,6 states that his competency comes from God. In fact, according to Paul, the very words that he used were taught by the Spirit:
This is what we speak, not in words taught us by human wisdom but in words taught by the Spirit, expressing spiritual truths in spiritual words.
Paul goes so far as to say that, even if angels preached something contrary to what he was preaching, they would be subject to eternal condemnation (Galatians 1:7,8).
Paul also stated that the instructions that he gave to the Thessalonians were given by the authority of the Lord Jesus (I Thess. 4:2), and that they were to stay away from those who did not live according to the teachings that they received from him and his associates (II Thess. 3:6). Moreover, in I Corinthians 14:37, Paul says specifically that what he is writing is the Lord's command.
In I Timothy 5:18, Paul quotes from Deuteronomy 25:4 and Luke 10:7 on an equal basis as though both are Scripture. This would indicate that in his next epistle to Timothy, Paul is referring both to the Old Testament and also to those portions of the New Testament that were then in existence when he states:
All Scripture is God-breathed and is useful for teaching, rebuking, correction and training in righteousness (II Timothy 3:16).
II Peter 3:15,16 specifically states that Paul's epistles are Scriptures:
Bear in mind that our Lord's patience means salvation, just as our dear brother Paul also wrote you with the wisdom that God gave him. He writes the same way in all his letters, speaking in them of these matters. His letters contain some things that are hard to understand, which ignorant and unstable people distort, as they do the other Scriptures, to their own destruction.
It is clear, therefore, that earlier in the same epistle (II Peter 1:20,21), the word "Scripture" refers to both the Old and New Testaments:
Above all, you must understand that no prophecy of Scripture came about by the prophet's own interpretation. For prophecy never had its origin in the will of man, but men spoke from God as they were carried along by the Holy Spirit.
