A total of 52 per cent of voters surveyed in a nationwide Ipsos poll conducted for Fairfax chose the coalition over Labor - down four percentage points from the last poll in November.
Labor's popularity on a two-party-preferred basis rose four percentage points to 48 in the same period.
The government's 52 per cent rating is less than that secured under Tony Abbott at the last election (53.5 per cent on a two-party-preferred vote).
Mr Turnbull's rating as preferred prime minister dipped five percentage points to 64 per cent, while Opposition Leader Bill Shorten's crept higher by one percentage point to 19 per cent.
The poll of 1403 people was taken between February 11 and 13.
Shadow attorney-general Mark Dreyfus said the wave of relief that swept the nation when former prime minister Mr Abbott was removed was now receding.
Voters were not seeing any new policies from Mr Turnbull.
"They're seeing a continuation of failed policies," he told ABC TV.
"What we're seeing is chaos in the ministerial ranks with departure after departure.
