A fluid dispensing instrument and method for placing a material in the uterine cavity and moving the material from the uterine cavity to the canals of the Fallopian tubes of a female. The instrument has an elongated probe carrying an expandable sleeve. A housing connected to the probe has a chamber for a container storing the material. A plunger is operable to move the container onto a needle and force the material through the probe and into the uterine cavity. In one form, an actuator is continuously moved into the housing to initially partially expand the sleeve member to displace part of the uterine cavity. Further movement of the actuator dispenses the material from the probe into the uterine cavity. Continued movement of the actuator fully expands the sleeve member to displace the entire uterine cavity and pump the material into the canals of the Fallopian tubes. After the sleeve member is contracted by releasing the fluid pressure applied thereto, the probe is removed from the uterine cavity.