CANBERRA - Australian voters appear to be turning away from Prime Minister Malcolm Turnbull's coalition government in the wake of the citizenship crisis embroiling parliament.

Turnbull's conservative Liberal-National Party coalition has lost ground to the opposition Labor Party, according to the latest Newspoll conducted for The Australian newspaper.

Labor leads the coalition 55 to 45 in two-party terms, while the coalition's primary vote has fallen from 35 to 34 percent since the citizenship scandal erupted.

The poll also found Turnbull's own personal rating had slumped. He now leads Labor leader Bill Shorten as preferred prime minister by just 2 percentage points, with his approval rating dipping five to 36 percent in the past two weeks. That compares with a lead of eight points just two weeks ago and 17 points at the end of August.

The latest results place Labor in its strongest overall position since Turnbull replaced Tony Abbott as prime minister in September 2015.

The poll was released as controversy over the country's parliamentary eligibility rules continued to rumble on.

Liberal backbencher John Alexander resigned at the weekend conceding he may also be a British citizen. He was the eighth MP to have been caught up so far in the citizenship crisis.

Australia's constitution bars from parliamentary office those who are eligible to be citizens of another country.

Last month Barnaby Joyce, who was the National Party leader and deputy prime minister, was forced to stand down and recontest his seat of New England in a by-election on Dec 2 after he was ruled ineligible by the High Court. Though born in Australia, he was conferred New Zealand citizenship by descent from his father.

Labor is in danger of also being drawn into the eligibility mire. Several of its MPs are facing pressure to clarify their status, with Turnbull saying at the weekend they, like any other MP, regardless of their party affiliation, may need to go to the High Court to do so.

Alexander's resignation means the coalition no longer has a majority in its own right in the House of Representatives but Turnbull said his government retained the support of the crossbench on matters of confidence and supply, and an election was not necessary.