The Uganda Women Parliamentary Association (UWOPA) wants President Museveni to appoint a woman for the position of vice president.
Currently the post is held by Edward Kiwanuka Ssekandi who succeeded Prof Gilbert Bukenya.
Dr Specioza Kazibwe was the last woman to hold the slot between 1998 and 2003.
The chairperson of UWOPA Pamela Kamugo Nasiyo said Museveni should appoint a woman vice president because other senior executive positions are held by men.
She said the judiciary is already led by men therefore it is only fair that women are appointed to leadership positions.
Kamugo called on the MPs to ensure that they re-elect Rebecca Kadaga as speaker of the 11th Parliament.
Kadaga, who has been speaker for 10 years, is expected to tussle it out with Jacob Oulanyah, the deputy speaker.
UWOPA also urged the National Unity Platform (NUP), the leading opposition party to elect a woman as leader of opposition.