Such calls represented a “coup against the constitution and an attempt to end the democratic experience”, he warned.
The US has led appeals to the country’s political leaders to rise above sectarian and ethnic divisions.
Government forces have been unable to recapture the territory seized by the rebels this month.
Almost half of the 300 US military advisers assigned to help the Iraqi security forces have arrived.
Fighting was reported to have continued on Wednesday, with an attack by rebels on the Balad airbase, about 80km (50 miles) north of Baghdad.
Meanwhile, the crisis in Iraq is being discussed by Nato leaders meeting in Brussels. They have been joined by US Secretary of State John Kerry, who has just returned from a two-day visit to Baghdad and Irbil.
In his weekly televised address, Mr Maliki called on “all political forces to reconcile” in the face of a “fierce terrorist onslaught”.
But the Shia prime minister gave no promise of greater representation in government for the minority Sunni Arab community, whose anger at what they say are his sectarian and authoritarian policies has been exploited by jihadist militants from the Islamic State in Iraq and the Levant (Isis).
Mr Maliki said forming an emergency administration that included all religious and ethnic groups would go against the results of April’s parliamentary elections, which were won by his State of Law alliance.
“The dangerous goals of forming a national salvation government are not hidden,” he said. “It is an attempt by those who are against the constitution to eliminate the young democratic process and steal the votes of the voters.”
Mr Maliki committed to start forming a new governing coalition by 1 July.
BBC Analysis: Richard Galpin, Baghdad
Mr Maliki used his weekly TV address to the nation to make it clear he will not be bulldozed into forming a government which does not take into account the result of the election in April.
He is signalling he intends following the normal constitutional mechanism for forming the new government in the coming weeks.
And that will give his alliance of Shia parties, known as the State of Law, the chance to build a coalition of its choice to secure a parliamentary majority and to select who will be the new prime minister.
It was Mr Maliki’s political rival Ayad Allawi who raised the issue of a national salvation government which the prime minister has so firmly rejected.
But it seems Mr Maliki is also firing a warning shot across the bows of the international community.
The United States in particular has been putting intense pressure on him to ensure a new government is formed as quickly as possible, with a broad spectrum of politicians.
One Western diplomat has said it should be a matter of days not weeks.
Speaking to the BBC in Dubai, UK Defence Secretary Philip Hammond criticised the current Iraqi government’s “deficit of inclusiveness”.
During his visit to Iraq, Mr Kerry warned that the country was now at a “critical moment” in its history. He promised that US support “will be intense and sustained and if Iraq’s leaders take the necessary steps to bring the country together, it will be effective”.
The 130 US military advisers are setting up a joint military operations room with the Iraqi army in Baghdad and another in the north.
US officials have made it clear that this is not a “rush to the rescue”, although the US advisers are in the position to call in air strikes against the militants if it is deemed necessary.
Their primary job is to assess the capabilities of the Iraqi forces and advise on what should be done, says the BBC’s Jim Muir in Irbil.
The US intelligence assessment is that the Sunni rebels spearheaded by Isis are capable of holding the territory they have captured.
Iraqi forces have tacitly recognised that, our correspondent adds. They have been unable to launch any strategic counter-offensives.
They are mainly focusing on two things – harassing the rebels from the air, mainly with attack helicopters, and building up their deployment for the defence of Baghdad, where troop numbers have been doubled.
The Iraqi military’s chief spokesman, Gen Qassim Atta, told a news conference on Wednesday that troops were in “full control” of Iraq’s largest refinery at Baiji. State TV showed reinforcements being flown by helicopter to the refinery, about 200km (130 miles) north of Baghdad, which supplies much of the country’s domestic fuel.
Iraqi military aircraft also attacked the town of Baiji. State television said 19 “terrorists” were killed, but witnesses said they were civilians.
Security forces and allied tribesmen meanwhile saw off an attack on the western town of Haditha, near a dam that supplies power to Baghdad.