Australia's beleaguered prime minister has ruled out throwing his job open to challengers with a leadership ballot to demonstrate his control over his government, warning his colleagues that voters crave stability.

Lawmakers within the ruling Liberal Party are pressuring Communications Minister Malcolm Turnbull, the party's former leader, and Foreign Minister Julie Bishop, Abbott's deputy, to challenge Abbott for the leadership in a ballot of Liberal lawmakers.

Abbott told reporters Tuesday that he is not prepared to initiate a ballot as a way to show how many of his party colleagues continue to support his leadership and how many do not.

He says his coalition was elected in 2013 because the previous center-left Labor Party government descended into chaos and infighting, changing its prime minister twice in three years.