* Approval rating of Australian PM hits 4-month low
* Government to meet for first time in six weeks
* Meeting follows series of by-election defeats
SYDNEY, Aug 13 (Reuters) - The personal approval rating of Australian Prime Minister Malcolm Turnbull fell to its lowest level in more than four months, a widely watched poll showed on Monday, adding pressure on Turnbull as he seeks to unite a fractured government.
A Newspoll for The Australian newspaper showed Turnbull's lead as preferred prime minister over opposition Labor leader Bill Shorten fell 4 percentage points in the past two weeks, a result that weakens his hand ahead of a critical meeting of the centre-right government on Tuesday. personal popularity has so far safeguarded his leadership in a country where leadership changes have become common in recent years when polls have shown the government on course for an election defeat.
"Turnbull is again on the back foot. If he can't regain the momentum and get through his centrepiece policies, those leadership questions will again emerge," said Haydon Manning, a political science professor at Flinders University in South Australia state.
Turnbull's Liberal-National coalition government still trails Labor, the Newspoll opinion poll showed, although the margin was unchanged at 49-51.
Australia's government will convene on Tuesday after a six-week recess, the first time it will meet since a series of by-election defeats late last month. results fuelled pressure on Turnbull to resolve more than a decade of battles over climate and energy policies and spur investment in new power supply, as well as to provide clarity over whether he intends to pursue corporate tax cuts despite polls showing voters oppose them.
Turnbull's coalition failed to win any of the five by-elections in July, defeats widely seen as an indication he faces an uphill task to be re-elected at a national poll due by May 2019.