Barack Obama, the US president, has said Iraq took "a promising step" forward with the designation of a new prime minister, replacing Nouri al-Maliki.
Obama said on Monday he and Joe Biden, US vice president, had spoken with Haider al-Ibadi, offering the US support, hours after Iraqi president tasked the main Shia coalition nominee with the role.
"The only lasting solution is for Iraqis to come together and form an inclusive government," Obama said, after criticism that Maliki has ruled divisively to advance Iraq's Shia majority.
"This new leadership has a difficult task to regain the confidence of its citizens by governing inclusively and taking steps to demonstrate its resolve."
Abidi was nominated for the job by the Shia National Alliance parliamentary bloc and later appointed by the president early on Monday during a brief ceremony broadcast live on television.
Maliki remains caretaker prime minister until Abadi can form a new government, which he has 30 days to do so.
In a message recorded earlier on Monday, Maliki said Abadi's appointment had "no value whatsoever."
"I want to reassure everyone that don’t worry, everything that happened today is meaningless and we will still be here. I urge all the Mujahedeen army fighter sand volunteers not to worry," Maliki said of attempts to replace him.
Al Jazeera's Jane Arraf, reporting from Erbil, said that Maliki would launch a legal case to prevent Abadi from taking office.
Allies of the incumbent PM called the attempt to remove him a "Kurdish and American conspiracy," Arraf said.
Iraqi state TV said the the electoral slate would hold a news conference, which will be attended by Maliki.
The deepening political tensions come as fighters from the Islamic State group made advances by capturing the town of Jalawla northeast of Baghdad, after defeating Kurdish Peshmerga troops.
This latest round of political infighting could hamper efforts to stem advances by the Sunni group.
The State of Law had won the most parliament seats in the April elections and Maliki had seen himself as keeping the post for a third term.
But has been accused by critics of steering the country toward a sectarian war.
No US strike plans
The Pentagon said on Monday that the US has no plans to expand its air campaign in Iraq beyond protecting American personnel in the city of Arbil and besieged Yazidi refugees.
"Our principal task to date, and what we are doing right now, is to protect US facilities and the citizens - American citizens - at those facilities," Lieutenant General William Mayville told reporters at the Pentagon. "There are no plans to expand the current air campaign beyond the current self defense activities."
Last week, US warplanes launched strikes to beat back fighters from the so-called Islamic State who had threatened to massacre the Yazidi religious minority and attack Arbil.