The move, which comes after months of political wrangling, is likely to be resisted by Nuri al-Maliki, who has rejected calls to drop his bid for a third term as prime minister.
New Prime Minister Haider al-Abadi called on Iraqis to unite against the "barbaric" campaign waged by Islamic State militants whose latest sweep through the north has caused alarm at home and abroad.
"We all have to cooperate to stand against this terrorist campaign launched on Iraq and to stop all terrorist groups," he said in remarks broadcast on state television just after the president asked him to form a government.
US Vice President Joe Biden commended Iraqi President Fouad Masoum in a phone call on Monday for selecting a new prime minister to replace Nuri al-Maliki and urged the timely creation of an inclusive government.
The two discussed the nomination of Haider al-Abadi as prime minister, the White House said in a statement about the call.
Biden also reiterated US support for Masoum as the guarantor of the Iraqi constitution, the White House said.
UN Secretary-General Ban Ki-moon on Monday welcomed what he described as "the forward movement toward government formation in Iraq" and praised the Iraqi president's decision to ask Haidar al-Abadi to form a new cabinet, the United Nations said. REUTERS For more details, watch Yazbek Wehbe's full report in the video above