Haider al Abadi still faces a threat closer to home, where his Shi'ite party colleague Nuri al Maliki has refused to step aside after eight years as premier that have alienated Iraq's once dominant Sunni minority and angered Washington and Tehran.
However, a senior government official said commanders of military forces that Mr Maliki deployed around Baghdad on Monday had pledged loyalty to President Fouad Masoum and to respect the head of state's decision to ask Mr Abadi to form a new government.
As Western powers and international aid agencies considered further help for tens of thousands of people driven from their homes and under threat from the Sunni militants of the Islamic State near the Syrian border, Secretary of State John Kerry said the US would consider requests for military and other assistance once Mr Abadi forms a government to unite the country.
Underscoring the convergence of interest in Iraq that marks the normally hostile relationship between Washington and Iran, the head of Tehran's National Security Council congratulated Mr Abadi on his nomination. Like Western powers, Iran has been alarmed by the rise of Sunni militants across Syria and Iraq.
Mr Abadi himself, long exiled in Britain, is seen as far less polarising, sectarian figure than Mr Maliki, who is also from the Shi'ite Islamic Dawa party.
Mr Abadi appears to have the blessing of Iraq's powerful Shi'ite clergy and "called on all political powers who believe in the constitution and democracy to unite efforts and close ranks to respond to Iraq's great challenges".
One politician close to Mr Abadi said the prime minister-designate had begun contacting leaders of major groups to sound them out on forming a new cabinet. The president said on Monday he hoped he would succeed within the next month.
Mr Maliki angrily dismissed Mr Abadi's nomination on Monday as illegal but there was no further sign of opposition yesterday.
While US officials have been at pains not to appear to be imposing a new leadership on Iraq, three years after US troops left the country, President Barack Obama was quick to welcome the appointment.
Wrangling over a new government since Iraqis elected a new parliament in April has been exploited by the Islamic State to seize much of the north and west.
Mr Obama has sent hundreds of US military advisers and last week launched air strikes on the militants after they made dramatic gains against the Peshmerga forces of Iraq's autonomous ethnic Kurdish region, an ally of the Baghdad authorities.
US officials have said the Kurds are also receiving direct military aid and US and British aircraft have dropped food and other supplies to terrified civilians, including from the Yazidi religious minority, who have taken refuge in remote mountains.
Mr Kerry said yesterday Mr Abadi could win more US military and economic assistance, adding: "We are prepared to consider additional political, economic and security options."