Abbott faced ridicule after naming the nonagenarian consort of Queen Elizabeth II a knight of the order of Australia last month, incensing members of his ruling coalition who were already dealing with falling poll numbers, policy backflips and an unpopular budget, AFP reported.
When asked by reporters if he had considered resigning, Abbott said "no" -- but admitted: "I accept that I probably overdid it on awards."
He said he believed he was the right person to lead the government after reports that some of his colleagues were under pressure to challenge him.
"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," he told the National Press Club in Canberra.
"Its the people that hire and frankly its the people that should fire."
Abbotts Liberal-National coalition romped to power in a September 2013 election but is now trailing the opposition Labor Party 46 to 54 percent, a Fairfax-Ipsos poll in The Sydney Morning Herald showed Monday.
The poll of some 1,400 people at the end of last week also found that Abbotts rating as preferred prime minister had slipped from 39 to 34 percent, while Labor leader Bill Shorten had climbed to 50 percent.
"I never came into politics to be popular," said Abbott, after being asked why people didnt seem to like him.
The dire polling follows a dismal result in a Queensland state election, which still hangs in the balance, but which delivered a thumping swing against the ruling conservative administration.
Abbott conceded the government had struggled to get its message across, as he promised a more consultative style of leadership.
"Look, weve had a rough couple of months, I accept that," he said.
"But, you know, when things are difficult the last thing you want to do is to make your difficulties worse."
Abbotts troubles have raised the prospect of a mid-term leadership challenge, and reports have suggested Communications Minister Malcolm Turnbull, Foreign Minister Julie Bishop, or Social Services Minister Scott Morrison could be the circuit-breakers.
But as The Australians editor-at-large Paul Kelly noted, there were "still no serious candidates".
A leadership challenge would revive memories of the sudden removal of then Labor prime minister Kevin Rudd in 2010 in a party room coup by his deputy Julia Gillard. Gillard was ousted by Rudd in 2013.