A longer section of melody that keeps reappearing in the music - for example, in a "theme and variations" - is often called a theme. Themes generally are at least one phrase long and often have several phrases. Many longer works of music, such as symphony movements, have more than one melodic theme.
The musical scores for movies and television can also contain melodic themes, which can be developed as they might be in a symphony or may be used very much like operatic leitmotifs (pg 77). For example, in the music John Williams composed for the Star Wars movies, there are melodic themes that are associated with the main characters. These themes are often complete melodies with many phrases, but a single phrase can be taken from the melody and used as a motif. A single phrase of Ben Kenobi's Theme19, for example, can remind you of all the good things he stands for, even if he is not on the movie screen at the time.