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.
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.
"It's the people that hire and frankly it's the people that should fire."
The poll of some 1,400 people at the end of last week also found that Abbott's rating as preferred prime minister had slipped from 39 to 34 per cent, 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 didn't 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, we've 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."
Abbott's 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.

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