Prime Minister Scott Morrison says he is not worried about the results of the latest poll, which has the government still behind the Labor Party on a preferred two-part basis.
The Fairfax-Ipsos poll gives Labor a preferred two-party advantage of 53-47 percent over the coalition, two points less than last month.
"We have been marked below the events of several weeks ago and that is understandable," Morrison told Channel 7 on Monday.
Morrison took the reins of Malcolm Turnbull last month after disunity within the Liberal party.
The Fairfax-Ipsos survey found that only 49 percent of voters believe that the prime minister has the confidence of his party, compared to 70 percent of Shorten.
However, there was some positive news for Mr. Morrison.
49% of voters consider the prime minister reliable, compared to 39% of Shorten.
And the former federal treasurer's economic credentials have a 66% voter rating, compared to 47% for the opposition leader.
The government is expected to face pressure this week with Labor and the Greens seeking to refer Interior Minister Peter Dutton to the Superior Court to verify whether he is violating the constitution because of his family's financial interest in two day care centers.
Mr. Dutton says his legal advice places his eligibility beyond doubt.
Labor leader Bill Shorten says the opposition will wait until he knows he has the support of some government parliamentarians to try to send Mr. Dutton.
An investigative report that expires on Wednesday will shed light on another issue affecting Mr. Dutton: his ministerial decisions to approve visas for two au pairs.
Liberal unrest is expected to continue, as party chairman Nick Greiner told ABC TV he did not see why the results of the preselection at the seat of former Prime Minister Tony Abbott of Warringah should not be publicly disclosed.
The result of another pre-selection, at the Wentworth headquarters vacated by Mr. Turnbull, is also expected to be aired in parliament.
Liberals shortlisted diplomat Dave Sharma, who does not live in the seat, despite Mr. Morrison backing a candidate.
Sharma faces a tough test against independent candidate Dr. Kerryn Phelps, who announced her nomination on Sunday.
The Speaker of the House of Representatives, Tony Smith, will issue the brief for the by-elections on October 20, Monday.
The government's credibility will also be scrutinized on Tuesday with an investigation into the controversial $ 444 million grant to the Great Barrier Reef Foundation, taking evidence from the administration of the foundation.
Labor will use parliament to seek details about the government's announcement of a royal commission in the elder care system, which the coalition has previously rejected.
Mr. Morrison's announcement on Sunday did not include the terms of reference, cost, time or who will be the actual commissioners.