The phrase "fulfilling the Law" appears Matthew 5:17-18, where it emphatically does not refer to any abolition of the Torah and law observance:
"Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. I tell you the truth, until heaven and earth disappear, not the smallest letter, not the least stroke of a pen, will by any means disappear from the Law until everything is accomplished. Anyone who breaks one of the least of these commandments and teaches others to do the same will be called least in the kingdom of heaven, but whoever practices and teaches these commands will be called great in the kingdom of heaven" (Matthew 5:17-18).
The same thought also occurs in ch. 7 which warns against those who DO NOT "do the will of God" (i.e. do not observe his commandments in the Law) but who call out to Jesus as "Lord, Lord" (cf. Romans 10:9) and prophesy in his name (cf. Romans 12:6, 1 Corinthians 14:5-39). They are called "workers of lawlessness" (7:23) because they are literally Law-less; they do not follow the Law. Matthew represents one side in a dispute in early Christianity on observing the Law; Paul (and the antinomians following him) represents the other side. The Jewish-Christian character of Matthew is well known, as are other early Christian books in the same vein (i.e. James, the Didache, the Ascents of James, the Kerygmata Petrou). Thus, the authority that Jesus gives to his apostles is rabbinical, of "binding and loosing" (cf. 16:19, 18:18), and salvation in Matthew is based on righteousness (Matthew 5:10, 20, 6:1, 33, 7:21-23, 21:32), how one acts and does the will of God, and not on faith, which is more prominent in John and Paul. In what looks like a response to the antinomians who believe that only faith is necessary, James similarly claims that "a person is justified by what he does and not by faith alone" (2:24). The Didache, the late first century-early second century catechism for Gentiles, similarly tells Gentiles that "if you are able to bear the whole yoke of the Lord (i.e. the commandments of the Law), you will be perfect. But if you are not able, then do what you can" (6:2), including dietary laws concerning which the Gentiles are told to "bear what you can". Yet only those who become "perfect" are truly saved: "All the time you have believed (i.e. faith) will be of no use to you if you are not found perfect (i.e. justified through righteousness) in the last time" (16:2). The Kerygmata Petrou also explains how Christianity is supposed to be Law-observant yet totally distinct from Judaism:
"For we say, that he is a worshipper of God, who does the will of God, and observes the precepts of his Law. For in God's estimation he is not a Jew who is called a Jew among men, nor is he a Gentile that is called a Gentile, but he who, believing in God, fulfills his Law and does his will, though he be not circumcised. He is the true worshipper of God, who not only is himself free from passions but also sets others free from them" (Rec. 5.34).
Similarly, the Preaching of Peter quoted by Clement of Alexandria (Stromata 6.5) states that "what belonged to the Greeks and Jews is old. But we, who worship God in a new way, in the third form, are Christians. For clearly, as I think, he showed that the one and only God was known by the Greeks in a Gentile way, by the Jews in a Jewish way, but in a new and spiritual way by us".
The idea in Matthew is not that Jesus rescinded the Law, but that he showed how it should properly be interpreted and followed. Thus the Pharisees, which are more of a vaguely understood foil to Jesus in Mark and John, are condemned in a uniquely detailed, and insult-laden way in Matthew, especially in ch. 23. Matthew does not condemn the Pharisees for following the Law or even adding their own oral law to it; he condemns them for lacking righteousness (5:20) and preventing others from attaining righteousness (23:13), by ignoring the most important laws of all (7:12). In fact, the principle noted here and in Paul and James (cf. Romans 13:9, Galatians 5:14, James 2:8) was also taught by the rabbis (cf. Sifra Qedoshim, 4; cf. also Philo, Specialibus Legibus 2.63) and did not originate with Jesus; the critique, as ch. 23 makes clear, is that the Pharisee rabbis do not follow such principles by their actions, thus they are "hypocrites". The Pharisees, btw, are seen not as they were in the early first century (at which time they were one small faction among many), but as they were in the post-A.D. 70 period, probably in the local community where the Matthean church existed side-by-side with non-Christian rabbinical Judaism and antinomian Christians. The book is polemically opposed to both groups, and David Sim (Apocalyptic eschatology in the gospel of Matthew, 1996, Cambridge University Press) has an interesting analysis that connects the Law-observant but anti-Pharisee and anti-Paulinist rhetoric of Matthew with localized religious rivalries between Jews and Christians in post-A.D. 70 Syria.
