Second Kings, Second Chronicles and Jeremiah describe the Babylonian destruction of Jerusalem and the First Temple. These events provide the biblical background for the mourning later associated with Tisha B'Av.
Lamentations gives voice to the grief of a devastated city. It became the biblical book most closely associated with Tisha B'Av and is traditionally read during the observance.
Numbers 13-14 tells the story of the spies sent into Canaan. Jewish tradition later associated the people's fearful response with the Ninth of Av. The biblical passage itself does not give that calendar date.
Zechariah refers to the fast of the fifth month. This reflects the practice of mourning the destruction of Jerusalem after the Babylonian exile.
The New Testament does not mention Tisha B'Av by name. The relevant passages instead concern Jesus' sorrow over Jerusalem and His warnings about the destruction of the Temple. Those warnings provide an important connection with the event that later became central to the observance.