However, the Government's 51 per cent to 49 per cent lead over the opposition is less than the survey's 3-percentage-point margin of error.
In Abbott's last news conference as Prime Minister, after he was ousted in a surprise leadership ballot in the ruling Liberal Party, he promised to make the transition to the new Administration "as easy as I can".
Abbott said: "There will be no wrecking, no undermining and no sniping."
But in his first media interview since then, Abbott contradicted new Treasurer Scott Morrison's version of events leading up to the leadership challenge.
Morrison has said he played no role in the challenge and that he warned Abbott's office days before the Turnbull challenge that resulted in his own promotion from Social Services Minister to the senior economics portfolio - regarded as the most prestigious after the Prime Minister.
Morrison also said he warned Abbott's office days ahead that "things were pretty febrile and they should be on high alert".
But Abbott told the Daily Telegraph there was no such warning.
"Not true, not true. Scott never warned anyone," Abbott told the newspaper in an interview published yesterday. "I'm afraid Scott badly misled people."
- AAP