Governor-General Quentin Bryce offered to resign to avoid any perception of bias now her son-in-law Bill Shorten is Opposition Leader.
But Ms Bryce will stay on after Prime Minister Tony Abbott asked that she serve out her full term.
"I have thanked her for her magnanimity but declined to accept her resignation," Mr Abbott said yesterday.
"I am grateful that she has kindly agreed to my request.
"Her agreement to stay on was a measure of her personal commitment to provide continuity at a time of political turbulence and she should be commended for her dedication to public service."
Ms Bryce is to keep her post until March, when she is due to retire.
Mr Shorten is married to Ms Bryce's daughter Chloe. They were married in 2009 and have three children.
It is not the first time the Governor-General's relationship with Mr Shorten has raised questions over conflict of interests.
In 2010, Ms Bryce was forced to seek legal advice from the Solicitor-General on whether her connections to Mr Shorten - then a minister in the Gillard government - could prove a point of contention in a constitutional crisis.
Mr Abbott said there was no need for the Governor-General to resign because the Government commanded the House of Representatives with a "significant margin".
"I believe it is only fit and proper that she be permitted to conclude her term and be accorded the appropriate farewell that her exemplary service merits," he said.
While it is thought there is no legal reason why Ms Bryce should have been forced to resign, the perceived public conflict of interests in any constitutional crisis would have been significant.