Members of the Yazidi sect fled there 10 days ago after fighters from Islamic State (IS) seized the town of Sinjar.
The US has been conducting air strikes to help stem the rapid IS advance in the north of the country.
On Monday, Iraq’s president asked MP Haider al-Abadi to form a new cabinet, snubbing the incumbent PM Nouri Maliki.
Mr Maliki called the nomination a “violation of the constitution”, 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 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.
An estimated 700,000 Yazidis have been displaced since IS militants took Sinjar from Kurdish forces defending the town, the UN says.
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”, with what looked like hundreds of dead people everywhere.
“You can imagine what it’s like when you land amongst 5000 people and can only take 10 or 20, and everybody tries to get on the helicopter,” Mirza Dinnay told the BBC.
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”.
President Obama stressed that there was no American military solution to the crisis – and that only an inclusive Iraqi government could unify the fight against the Islamists.
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.
In a televised address, he added that he would “fix the mistake”.
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.