Haider al-Ibadi, the deputy speaker of parliament from al-Maliki's Shiite Dawa party, was selected by President Fouad Massoum to be the new prime minister and was given 30 days to present a new government to lawmakers for approval.
U.S. President Barack Obama called al-Ibadi's nomination a "promising step forward" and he urged "all Iraqi political leaders to work peacefully through the political process."
But al-Maliki, who has been in power for eight years, defiantly rejected al-Ibadi's nomination as prime minister. In a speech after midnight Sunday, he accused Massoum of blocking his reappointment as prime minister and carrying out "a coup against the constitution and the political process."
In another speech broadcast Monday night, al-Maliki insisted al-Ibadi's nomination "runs against the constitutional procedures" and he accused the United States of siding with political forces "who have violated the constitution."
"Today, we are facing a grave constitutional breach and we have appealed and we have the proof that we are the largest bloc," al-Maliki said.
"We assure all the Iraqi people and the political groups that there is no importance or value to this nomination," he added.
But despite angrily insisting he should be nominated for a third term, al-Maliki has lost some support with the main coalition of Shiite parties. His critics say al-Maliki contributed to Iraq's political crisis by monopolizing power and pursuing a sectarian agenda that alienated the country's Sunni and Kurdish minorities.
In welcoming the new Iraqi leadership amid the country's worst crisis since U.S. troops withdrew in 2011, Obama said the only lasting solution is the formation of an inclusive government.
"These have been difficult days in Iraq," Obama said while on vacation on Martha's Vineyard. "I'm sure there are going to be difficult days ahead."
The nomination of al-Ibadi came hours after al-Maliki deployed his elite security troops in the streets of Baghdad. Hundreds of his supporters were escorted to a popular rally site by military trucks, raising fears he might try to stay in power by force.
"We are with you, al-Maliki," they shouted, waving posters of him as they sang and danced.
Al-Ibadi, the former minister of communications from 2003-04, pledged to form a government to "protect the Iraqi people." He was nominated after receiving the majority of votes from lawmakers within the Iraqi National Alliance, a coalition of Shiite parties.
A peaceful transition is looking increasingly unlikely, given al-Maliki's reputation for having replaced many senior Sunni officers with less-experienced, more loyal Shiite officers.
"One of the major concerns (the U.S.) had in 2010 is the degree to which al-Maliki was trying to coup-proof his military," said Richard Brennan, an expert on Iraqi special forces at Rand Corporation and former U.S. Department of Defense policymaker. "The U.S. worked hard with the military to make them understand that loyalty had to be to country, not to al-Maliki, but al-Maliki cut the forces to replace competent people with less-competent people loyal to him."
Vice President Joe Biden called Massoum to commend him for meeting a "key milestone" in nominating al-Ibadi. Prior to al-Ibadi's nomination, U.S. Secretary of State John Kerry said in Sydney "there should be no use of force, no introduction of troops or militias into this moment of democracy for Iraq."
Kerry added a new government "is critical in terms of sustaining the stability and calm in Iraq," and that "our hope is that Mr. Maliki will not stir those waters."
Iranian President Hassan Rouhani, who has expressed fears that Iraq will fragment unless al-Maliki leaves power, expressed his concern about the political crisis in Baghdad in a call with newly elected Turkish President Recep Tayyip Erdogan.
"It is important for Iran that a person approved by a majority of the representatives of the people in the Iraqi parliament takes power and begins his legal actions in Iraq."
The U.S. weapons being directly sent to Irbil are very limited in scope and number, and mostly consist of light arms like AK-47s and ammunition, a Kurdish government official and a senior Pentagon official said.
The Kurdish official said the weapons are being sent through U.S. intelligence agencies, and not the Pentagon or the State Department. Lt. Gen. William Mayville, the operations director for the Joint Chiefs of Staff, said the Pentagon was looking at other ways to help the Kurds.
But the Kurdish official said the U.S. lethal aid is still not enough to battle the militants, even though peshmerga and other Kurdish forces were supplemented with similar munitions from Baghdad over the weekend. Neither official was authorized to discuss the U.S. arms by name and spoke on condition of anonymity.
U.S. airstrikes have reinvigorated Iraqi Kurdish forces battling the Islamic State and on Sunday, the Kurdish peshmerga fighters retook two towns Makhmour and al-Gweir, some 28 miles (45 kilometers) from Irbil from the Sunni militants in what was one of their first victories after weeks of retreat.
The successes were balanced out, however, by news of a defeat in the far eastern Diyala province where Kurdish forces were driven out of the town of Jalula after fierce fighting against the militants. The militants blasted their way into the town using a truck bomb followed up with several suicide bombers on foot, said a police officer and an army official, adding that at least 14 Kurdish fighters were killed.
Obama warned Saturday the new campaign in Iraq requires military and political changes and "is going to be a long-term project."
The move to directly arm the Kurds underscores the level of U.S. concern about the Islamic State's gains particularly at a time when there is such significant turmoil within the central government in Baghdad.
Turkey has warned al-Maliki that his actions threaten to deepen a crisis in Iraq and called on him to support Massoum and urged lawmakers to avoid actions that "deepen the turmoil in Iraq."
In recent months, support for al-Maliki has waned, not only among politicians, but also from Iraq's Shiite religious establishment and particularly, its most revered cleric Grand Ayatollah Ali al-Sistani, who is closely linked with Iraq's biggest ally, Iran.
Disunity is not exclusive to the Shiite coalition, however. Sunni political parties, once-superior under ousted leader Saddam Hussein, have also been at odds in recent months as they try to reassert themselves in al-Maliki's government while distancing themselves from the Sunni militant onslaught that has killed thousands.
It also has displaced more than 1.2 million people, said Kieran Dwyer, spokesman for the U.N. Office for the Coordination of Humanitarian Affairs.
"All of this amounts to a humanitarian catastrophe," Dwyer told reporters by phone from Irbil.
U.S. Agency for International Development Administrator Rajiv Shah said the team will help speed food, water and other life-saving supplies to Iraqis. Much of the assistance will go to thousands of members of an Iraqi religious minority group known as Yazidis who have been trapped on a mountaintop in northwest Iraq to escape certain death by Sunni militants with the Islamic State group.
U.S. Central Command said Monday that it had conducted a fifth airdrop of food and water for thousands of members of the Yazidis.
While violence has straddled the Syrian-Iraqi border in recent months and seeped deep into the heart of some of Iraq's most ancient and strategically located cities, some are warning that if a political solution is not found soon, Baghdad risks getting drawn into the war.
"Iraq could become a tale of two prime ministers, each claiming to have the constitution supporting their claim," said Ramzy Mardini, an Iraq expert with the Washington-based Atlantic Council. "It will either end by legal venue or by conflict."
Associated Press writers Sinan Salaheddin in Baghdad, Matthew Lee and Lolita C. Baldor in Sydney, Lara Jakes and Ken Dilanian in Washington, Nedra Pickler and Julie Pace in Martha's Vineyard, Mass; Edith M. Lederer at the United Nationsl, and Suzan Fraser in Ankara, Turkey, contributed to this report.