The embattled premier has grown increasingly isolated, with Iraqi politicians and much of the international community lining up behind Haider Ibadi, a fellow member of his Shi'ite Dawa party tasked by the president with forming a new government that can unite the country in the face of an onslaught by Sunni militants.
But Mr Maliki said in his weekly televised address to the nation: that holding on to the premiership "is an ethical and patriotic duty to defend the rights of voters."
He added: "The insistence on this until the end is to protect the state."
Mr Maliki vowed to take legal action against President Fouad Massoum for carrying out "a coup" against the constitution.
He added: "Why do we insist this government continue and stay as is until a decision by the federal court is issued? It is a constitutional violation - a conspiracy planned from the inside or from out."
Iraqi troops imposed heightened security in Baghdad yesterday as international support mounted for a political transition.
Tanks and Humvees were positioned on Baghdad bridges and at major intersections, with security personnel more visible than usual. About 100 pro-Maliki demonstrators took to Firdous Square in the capital, pledging their allegiance to him.
Widespread discontent with Mr Maliki's divisive rule has reached the point where both Saudi Arabia and Iran - regional rivals often bitterly divided over Iraq - have expressed support for Mr Ibadi.
The US, EU and the UN have also expressed support for new leadership.
But Mr Maliki, whose bloc won most votes in April's elections, has thus far refused to step down, and rejected Mr Ibadi's appointment, saying it was unconstitutional.
Mr Ibadi was selected by the main Shi'ite alliance, which includes Mr Maliki's bloc, but the Islamic Dawa party says Mr Ibadi "only represents himself".
Mr Maliki said security forces should not get involved in politics, but raised the spectre of further unrest by saying Sunni militants or Shi'ite militiamen might don military uniforms and try to take control of the streets.
He said: "This is not allowed because those people, wearing army uniforms and in military vehicles, might take advantage of the situation and move around and make things worse."
The turmoil stems from the rapid advance of the Islamic State group and allied Sunni militants across northern and western Iraq in June.
Fuelled by widespread Sunni discontent with Mr Maliki's rule, the insurgents seized Iraq's second largest city, Mosul, and routed the beleaguered armed forces.
Thousands of people have been killed and more than 1.5 million displaced by the violence.
The militant advance slowed as they approached Baghdad and other majority Shi'ite areas but the capital still sees near-daily attacks.
A car bomb struck a police a checkpoint in western Baghdad yesterday, killing six people, including four policemen.
A separate car bomb killed four people in the city's western Baiyaa neighbourhood.