Support for the Coalition rose three points, while Labor fell three points, the poll published by News Corp showed.
Both parties were tied on a primary vote of 38 per cent.
In two-party terms, the Coalition made its single largest fortnightly gain in its 18 months in power, rising to 47 per cent.
The opposition however remains in a commanding two-party-preferred position of 53 per cent. The Greens were unchanged at 12 per cent.
The latest poll also showed 77 per cent of those surveyed consider Mr Abbott arrogant, and only one-third of them believe he is in touch with voters.
Voters continued to rank opposition leader Bill Shorten as a better prime minister, by 43 per cent to 35 per cent.