"I have therefore submitted to the Chief Government Whip [Philip Ruddock] a motion to spill the leadership positions of the Federal Parliamentary Liberal Party. The spill motion should be considered via a secret ballot as the first item of business in our Party Room meeting," Simpkins said in an email to his colleagues, which circulated on social media.
Simpkins added in the email that he wanted to make sure that "economic vandals do not get back into power and our children and grandchildren are not left to pay Labor's bill."
Following Simpkins' statement, Abbott issued a press release published on his website, saying that he will stand together with Julie Bishop against the spill motion.
"I have spoken to Deputy Leader Julie Bishop and we will stand together in urging the Party Room 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," the statement reads.
The Australian prime minister's rating has fallen sharply since the end of 2014 over his policy and personal gaffes.
Abbott's party members have long accused him of being unwilling to listen to other opinions while making decisions, but until now the accusations were anonymous.