Did Jesus abolish the law?

One difficulty of Christian theology is that of explaining the role of the Jewish law under the new covenant. Among the mixed messages that we get on this topic are two apparently contradictory statements about whether Jesus abolished the law.

Jesus himself described his mission as fulfilling the law, but not abolishing it:

Do not think that I have come to abolish the law; I have come not to abolish but to fulfill. [Matthew 5:17, NRSV]

However, Ephesians says that Jesus abolished the law:

He has abolished the law with its commandments and ordinances… [Ephesians 2:15a, NRSV]

So did Jesus abolish the law or not?