Abbott has been fighting for his job after poor poll ratings and a series of policy backflips spurred some MPs from his conservative Liberal Party openly to attack him, calling for a leadership "spill" on Tuesday.
The motion aims to declare the positions of party leader and deputy leader currently occupied by Abbott and Deputy Prime Minister Julie Bishop vacant so the party room, or members of both houses of parliament, can vote for new candidates.
"The last thing Australia needs right now is instability and uncertainty," he told reporters.
"On reflection, and after talking to my colleagues, I've decided that the best thing we can do is deal with the spill motion as quickly as possible and put it behind us," he said.
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The meeting of the governing Liberal Party will be held tomorrow morning, 24 hours earlier than scheduled, the Australian leader said.
"The only question for our party is do we want to reduce ourselves to the level of the Labor Party in dragging down a first-term prime minister," he added.
Prime minister Kevin Rudd was ousted by his deputy Julia Gillard in 2010. He later returned the favour and stormed back to power in 2013 shortly before losing the election to Abbott's coalition.
Abbott's comments came just hours after Communications Minister Malcolm Turnbull, seen as one of the main contenders for the leadership, broke his silence early today.
"I'm in the cabinet, I support the prime minister. You don't have to keep on saying that all the time," Turnbull, who once lost a leadership tussle with Abbott by one vote when the Liberals were in opposition, told a Channel Ten reporter.