Mr Natuman is on a two-year suspended sentence after pleading guilty to conspiring to pervert the course of justice.
The charge was in relation to a bitter dispute that engulfed the police force in 2014.
Mr Natuman, as then-prime minister, ordered the then-commissioner, Aru Maralau, to stop a police team from investigating other high-ranking officers accused of mutiny.
The Vanuatu Daily Post reported the heads of five different political parties had joined forces and yesterday signed a solidarity agreement to call for Mr Natuman's removal and they claim 18 government MPs are in support of the move.
They said it was unfair that Mr Natuman had been allowed to keep his portfolio despite his conviction.
MPs who signed the agreement include Sato Kilman, Ishmael Kalsakau, Marc Ati, Gracia Chadrack and Jay Ngwele.
The group also called for a review of tax reforms introduced by Charlot Salwai's government.