The Morrison government is being urged to set up a real-time count of Australian women killed by violence, similar to the national road toll.

After the new Senate called on the Coalition to set up an "official real-time" toll of women killed by violence during its first full day of sitting last week, Greens senator Larissa Waters has written to Minister for Women Marise Payne, asking the government to act.

Senator Waters, who sponsored the Senate motion on the toll, said a central point for counting the number of women who are killed would mean the "horrific statistic" stayed firmly in the minds of decision makers.

Larissa Waters has written to Minister for Women, Marise Payne, asking her to set up a national toll that tracks the deaths of women killed by violence. Credit:Alex Ellinghausen

Advocacy group Our Watch says on average, one woman a week is murdered by her current or former partner in Australia.