The ultimatum has put many Iraqi families in a desperate situation and non-governmental organisations (NGOs) are worried as displacement camps could not cope with all the internally displaced people (IDPs) that this ultimatum might trigger.
"Kadhimiya and Shu'ala districts are the most affected. Dozens of Sunnis have been assassinated in their homes since the second attack on Samara mosque on 13 June. Neighbours are invading homes and killing people without remorse," said Abdallah Seif Salman, president of the Iraq Aid Association (IAA).
"Many families are being kidnapped as soon as they leave the area, or the men are being killed by militias. Something should be done to protect these families urgently," Salman added.
Unofficial estimates are that around 400 families have become displaced since the recent Samara bombing.
The Ministry of Displacement and Migration said the figure could be higher because sectarian violence had escalated in the past few days, and there was serious concern for these families.
"There are two camps on the outskirts of the capital where threats were made two days ago. Families were told to leave or militants would kill everyone, and this caused panic," said a Ministry of Displacement and Migration media officer who preferred to remain anonymous for security reasons.
"We urge all parties to prevent the death of innocent civilians and their displacement, as NGOs and our Ministry cannot cope any more," the officer added.
Nowhere to go
The lack of medical care, food and water has meant many provinces are refusing to welcome any more people fleeing their homes. The newly displaced are having difficulty finding a place to stay, and have to sleep rough, aid workers said.
"In the past three days you could see families sleeping rough or even on farms on the outskirts of the capital, without protection or supplies. Yesterday a family of five were killed as they fled the Shu'ala District," said Salman.
"NGOs are concerned about how to bring supplies into the displacement camps as violence is increasing and we are in a dangerous situation," he said.
"Some families are able to get assistance from relatives in various parts of the country but this displacement has reached such a level now that many governorates are closing their doors to the displaced. They might have to flee to the border to keep their families alive, and if that happens, there will be a humanitarian disaster in Iraq," the Ministry of Displacement and Migration media officer said.
Deaths up in past four days
Local morgue officials said the number of deaths reported in the last four days had nearly doubled, with many bearing signs of torture.
In response to Shia militia attacks after the second Samara bombing, Sunni insurgents have increased their attacks on Shia districts, attacking houses and killing anyone inside, including children and women, observers said.
"We call on both sides for calm and for their leaders to stop the sectarian killings and enforced displacements. This will just postpone peace in Iraq and bring more suffering," said Lt-Col Ali Hazim, senior officer at the Ministry of Interior.
On 16 June, the UN-affiliated International Organization for Migration (IOM) appealed for US$85 million to assist hundreds of thousands of IDPs in Iraq. The Geneva-based organization has warned that large numbers of people will be forced to flee Iraq, unless the international community provides the funds to care for them.