Tens of thousands of civilians remain trapped by militants on a mountain in northern Iraq and need "life-saving assistance", the United Nations warns.
Members of the Yazidi sect fled there 10 days ago after fighters from Islamic State (IS) seized the town of Sinjar.
US air strikes continued on Tuesday, with a drone targeting an IS mortar near Kurdish troops, the Pentagon said.
On Monday, Iraq's president asked Haider al-Abadi to form a new cabinet, snubbing the incumbent PM Nouri Maliki.
Mr Abadi's appointment came after months of political infighting, which analysts say is partially to blame for Iraq's inability to effectively fight the IS threat.
Politicians had been unable to form a government since April's parliamentary elections, which were won by Prime Minister Maliki.
IS fighters have seized large swathes of northern Iraq and Syria in recent months, forcing tens of thousands of people from religious minorities to flee their homes.
Analysis: Jim Muir, BBC Middle East correspondent
Mr Abadi is certainly off to a flying start, given the near-universal relief that an alternative to the contentious Mr Maliki has finally emerged.
But he faces a gargantuan task.
Pulling the fragments of Iraq back together, and especially bringing the suspicious Sunnis back on board, is going to take a lot more than pious words and good intentions.
UN Secretary-General Ban Ki-Moon urged countries to do more to help Iraqi civilians.
"The plight of Yazidis and others on Mount Sinjar is especially harrowing," he said.
An estimated 20,000 to 30,000 people remain trapped on Mount Sinjar without food, water or shelter said the UN's Adrian Edwards in a statement.
There are now an estimated 1.2 million internally displaced Iraqis, he added.
Keiran Dwyer, who works for the UN's office for humanitarian affairs in Irbil, told the BBC that some Yazidis had managed to escape from the north side of the mountain in the last 72 hours and cross the River Tigris into Syria, where they were receiving help.
But a Yazidi relief worker, who was on board an Iraqi Air Force helicopter evacuating the trapped refugees, described the situation as "a genocide" and said that he had seen what looked like "hundreds" of dead bodies on the ground.
"You can imagine what it's like when you land amongst 5,000 people and can only take 10 or 20, and everybody tries to get on the helicopter," Mirza Dinnay told the BBC.
In other developments in Iraq on Tuesday:
- Iran has officially announced its support of the new Prime Minister designate Haider al-Abadi.
- A Kurdish government helicopter delivering aid has crashed on Mount Sinjar, killing the pilot and injuring a journalist for the New York Times. The survivors were taken to Irbil, the paper confirmed. There are also reports that an Iraqi MP was injured.
- US Vice-President Joe Biden has urged the leader of Iraq's Kurds, Massoud Barzani, to work with Mr Abadi.
- The Vatican has urged Muslim leaders to condemn the actions of IS fighters in Iraq. They have persecuted many of Iraq's minorities, including Christians.
The US, Britain and France have been delivering humanitarian aid to the Yazidis.
Over the last five nights, US and UK air crews have air-dropped more than 310 bundles of food, water and medical supplies, and delivered almost 72,740 litres (16,000 gallons) of water and 75,000 meals, the US government says.
The US has also reportedly begun supplying weapons to the Kurdish forces, known as Peshmergas, who have been fighting IS in the north.
Earlier, US President Barack Obama described the nomination of Mr Abidi as "a promising step forward".
But he also said the new leadership had a "difficult task to regain the confidence of its citizens by governing inclusively and taking steps to demonstrate its resolve".
The US has been reluctant to mobilise support while the government was led by Mr Maliki, a Shia seen by many as fuelling ethnic and sectarian tensions that boosted support for the Sunni militants, the BBC's Barbara Plett reports from Washington.
Mr Maliki has condemned the move to replace him, saying it would lead the country into a political crisis.
Mr Maliki called the nomination a "violation of the constitution" and vowed to "fix the mistake", but on Tuesday ordered security forces not to intervene in the political crisis.
In a statement published on his official website, Mr Maliki said security forces should instead focus on defending the country.
Mr Ban also urged Iraqi security forces not to intervene in the political dispute between Mr Maliki and the new nominee.
"It is imperative that the security forces refrain from intervening in the political process," he said.
On Monday, IS militants seized the town of Jalawla, north-east of Baghdad, after weeks of clashes with Peshmergas.
The rebels already control a number of strategic northern places including Iraq's largest dam, located near the city of Mosul.
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