The move comes after Abbott's much-ridiculed decision to award Britain's Prince Philip a knighthood sparked two weeks of turmoil in his Liberal Party, exposing discontent over months of policy failings and plunging poll figures.
"I think we must bring this to a head and test the support of the leadership," West Australian Liberal MP Luke Simpkins said in an email to colleagues announcing he will initiate a challenge.
"The reality is people have stopped listening to the prime minister," Simpkins later told Sky News, ahead of a meeting of the 102 Liberal parliamentarians next Tuesday where the secret ballot will take place.
Abbott hit back immediately, saying he had the support of his deputy Julie Bishop, whose strong performance as foreign minister had seen her touted as one of the contenders for the leadership.
"They are asking the party room to vote out the people that the electorate voted in," the prime minister said.
Abbott rose to power promising stable government and an end to the brutal internal warfare that undermined the previous Labor administration, but amid plunging popularity and policy reversals, now finds himself in a similar position.
Under Labor, Julia Gillard first ousted prime minister Kevin Rudd in 2010 only to be overthrown herself three years later by Rudd, who was then defeated in elections that installed Abbott as leader.
"We are not the Labor Party... and we are not going to repeat the chaos and the instability of the Labor years," Abbott said, adding that he and Bishop would "stand together in urging the party room to defeat this particular motion".
"We have a strong plan... and we are determined to get on with it," he said.
Simpkins appealed to the best interests of the country in asking the party room, made up of 102 Liberal members of the lower and upper houses of parliament, to "either endorse the prime minister or seek a new direction".
Chief government whip Philip Ruddock confirmed he had received notice of the leadership "spill" move and that it would be on the agenda at Tuesday's Liberal Party meeting in the capital Canberra.
Earlier this week several lawmakers openly revolted against the premier and called for a leadership vote.
Abbott's personal decision to award 93-year-old Prince Philip a knighthood "was for many the final proof of a disconnection with the people," Simpkins said.
If the leadership is declared vacant, the favourite for the prime ministership is Communications Minister Malcolm Turnbull -- who led the party before Abbott ousted him by a single vote in 2009.