Mr. Ban had called on all Iraqi political parties to work towards the formation of a new Government that would be able to confront the threat from the armed group, the Islamic State (IS).
The UN, with international and national partners, is studying the possibility of opening a humanitarian corridor to try to extract people from this area, the spokesperson said.
Attacks by IS have displaced hundreds of thousands of people. The situation is particularly dire on Jebel Sinjar, or Sinjar Mountain, where an estimated 50,000 people are believed to be trapped since ISIL displaced them from their homes more than one week ago.
The mountain is like a camelback that is 100 km long and about 10 km wide, with a large and rocky, barren hilltop, according to Kieran Dwyer, head of communications for the UN Office for the Coordination of Humanitarian Affairs (OCHA).
Speaking to reporters by phone from Erbil, he said that people are trapped in multiple locations on the mountain, with those on the south side more exposed to the armed groups.
“We can confirm that in the last 72 hours, some thousands of people have been able to escape from the mountain with assistance of Kurdish security forces and others,” he said.
Most of the people who escaped were from the north side of the mountain, which is close to the border with Syria, and from there, they moved by foot, about a 7-hour walk, or sometimes with the help of vehicles, to get to a point on the Tigris river, and then back into Iraq.
Mr. Dwyer stressed that the situation on the mountain, particularly for young children and the elderly, is absolutely dire with very little vegetation to provide shelter from the searingly hot temperatures reaching 45 degrees Celsius, 110 plus degrees Fahrenheit.