Embattled Australian Prime Minister Tony Abbott will face a party vote on his leadership early next week, after disgruntled government members openly demanded a challenge.

A member of Abbott's ruling conservative Liberal Party, Western Australian MP Luke Simpkins, sent an email to colleagues on Friday to announce he will move the vote at a scheduled party meeting in Canberra on Tuesday.

Abbott responded directly to the challenge, issuing a statement saying that he and his deputy, Foreign Minister Julie Bishop, would not step down.

"I want to make this very simple point. We are not the Labor Party ... and we are not going to repeat the chaos and the instability of the Labor years," his statement said, referring to the previous government which suffered through two changes of leadership during its six years in power.

"So I have spoken to Deputy Leader Julie Bishop and we will stand together in urging the partyroom to defeat this particular motion and in so doing, and in defeating this motion, to vote in favour of the stability and the team that the people voted for at the election," Abbott said.

"We have a strong plan. It's the strong plan that I enunciated ... this week and we are determined to get on with it, and we will."

Failing policies

Abbott has faced a torrent of criticism in recent weeks over policy decisions ranging from his handling of the economy to awarding an Australian knighthood to Queen Elizabeth's husband, Prince Philip.

No member of the government has so far indicated a direct challenge to Abbott, although most media attention has focused on Communications Minister Malcolm Turnbull, a former party leader toppled by Abbott.

Opinion polls have consistently shown voters prefer Turnbull to lead the party, but his support for environmental steps against carbon alienated some on the party's right.

Source: Al Jazeera and agencies