Thousands of people have been displaced by the Sunni militants' advance in northern Iraq. Photo: Reuters
Security forces loyal to Iraqi PM Nouri Maliki have appeared in force in the capital Baghdad after he went on state TV to criticise the president.
Maliki is seeking a third term but has faced calls to step down amid the jihadist insurgency in the north.
The US, which has urged Iraq to form an inclusive government, issued a statement backing President Fuad Masum.
Earlier, Iraqi Kurds appealed for international military aid to help defeat the Islamist militants.
The US has already launched four rounds of air strikes targeting Islamic State (IS) fighters near Irbil, the capital of Iraqi Kurdistan.
A Kurdish official said recent US air strikes on IS militants in Nineveh province had helped the Kurdish Peshmerga fighters retake the towns of Gwer and Makhmur after heavy fighting.
US air strikes have been launched from an aircraft carries in the Gulf. Photo: AP
In his televised address, Maliki said he intended to take President Masum to court for violating constitutional rules.
Maliki's coalition won the most seats in April's elections but parliament has not agreed to give him a third term and President Masum has declined to intervene.
Maliki said Masum had missed a deadline for asking the biggest political bloc to nominate a prime minister.
"This attitude represents a coup on the constitution and the political process in a country that is governed by a democratic and federal system," Maliki said.
"The deliberate violation of the constitution by the president will have grave consequences on the unity, the sovereignty, and the independence of Iraq and the entry of the political process into a dark tunnel."
Within an hour, Shia militiamen and security forces loyal to Maliki appeared at key centres in Baghdad. There were no reports of violence.
Critics say Maliki, a Shia, has precipitated the current crisis through sectarian policies and there have been calls by Sunnis, Kurds, and even fellow Shia for him to stand down.
The West has also piled pressure on Iraq's leaders to form a power-sharing government in the face of Sunni militants who now control a vast swathe of the country.
In Washington, deputy state department spokesman Marie Harf said it was "closely monitoring" the situation in Iraq.
"The United States fully supports President Fuad Masum in his role as guarantor of the Iraqi constitution," she said.
"We reaffirm our support for a process to select a prime minister who can represent the aspirations of the Iraqi people by building a national consensus and governing in an inclusive manner."
Earlier on Sunday, Kurdish forces said they had regained Gwer and Makhmur.
It is the first time Kurdish forces have regained ground from IS since US military action was authorised on Thursday.
In western Iraq, minority religious groups, such as the Yazidis, have been forced from their homes, prompting international aid drops.
Witnesses told the BBC that thousands of refugees near Sinjar had escaped to safer areas.
The president of the Kurdish regional government in Iraq, Massoud Barzani, made his plea for more weapons while speaking alongside French Foreign Minister Laurent Fabius, who was in Iraq for crisis talks with Iraqi and Kurdish officials.
"We are not fighting a terrorist organisation, we are fighting a terrorist state," Barzani said.
"The weapons they possess are more advanced than what the Peshmerga have."
Fabius later said that France would look into the possibility of supplying equipment to the Kurds.
The US air strikes have been the first direct American involvement in a military operation in Iraq since their withdrawal from the country in late 2011.
US President Barack Obama authorised the strikes last week after members of the Yazidi sect were forced to flee Sinjar into the surrounding mountains.