Delivering a key speech at the National Press Club in Canberra on Monday, Abbott made it clear that he was not considering stepping down.
"Let me make it absolutely crystal clear, we were elected in 2013 because the Australian people rejected chaos. And we are not going to take them back to that chaos. It's the people that hire and frankly it's the people that should fire," he said.
Abbott has repeatedly been slammed for his broken electoral promises, his inability to deal with policy backflips, and his government's unpopular budget.
The pressure especially intensified last week, when even his big-name supporters, including Australian-born media magnate Rupert Murdoch, publicly lashed out at Abbott's controversial decision to make Britain’s Prince Philip a knight.
Abbott's eyebrow-raising reintroduction of the notion of peerages last year sparked anger that he remains out of touch with national sentiment.
According to an opinion poll of about 1,400 people released late last week, voter approval for Abbott nosedived to 27 percent, while Labor opposition leader Bill Shorten's approval rating climbed to 44 percent.
The dismal survey came after an embarrassing result for the Liberal National Party, which is closely aligned to Abbott’s Liberal-National coalition.During the 2015 Queensland state election on January 31, the party lost its largest political majority in Australia's history after just one term in office.
The result fuelled a possible party revolt against Abbott's leadership after the government slammed the result of the elections as "catastrophic".