Huge numbers have already fled eastwards in recent weeks
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The UN says 20,000 people have fled Pakistan's tribal area of Bajaur for Afghanistan amid fighting between troops and militants in recent months.
The UN's refugee agency says almost 4,000 families have crossed north-west into Afghanistan's Kunar province.
The army began a sustained campaign against militants in Bajaur nearly two months ago.
Some 300,000 others have fled east within Pakistan in recent weeks with many of them living in temporary camps.
The military says it has killed more than 2,000 militants in the fighting.
Cross border attacks
The UN's High Commissioner for Refugees (UNHCR) believes that the majority of the refugees who have fled into Afghanistan will return home after the fighting stops in the Federally Administered Tribal Areas (Fata).
Announcing its estimates of the numbers of people who have crossed the border into Afghanistan, the UNHCR in Afghanistan said in the last two weeks alone, more than 600 families had left Pakistan for Kunar.
A spokesman said the organisation would look out for the welfare of the displaced if they were unable to return home before winter sets in.
"It's very difficult to predict the security situation on the other side of the border but what we hope is that the security gets better and people will be able to go back," Nadir Farhad told Reuters news agency.
"But if it continues, we will definitely provide them with... assistance... so we can get them through the winter months."
"They have mainly been provided accommodation by relatives and friends but some 200 families are already living without shelter" he said.
The UNHCR says around 70% of the families are from Pakistan but the rest are Afghans who have been living in Pakistan.
In the past, Afghan refugees have crossed the border the other way, around four million escaping violence and seeking refuge in Pakistan in the 1980s and 1990s, but more than half have since returned to Afghanistan.
Recently the UNHCR asked donors for more than $17m (39.4m) in aid to help about 250,000 people displaced by fighting and floods in north-western Pakistan.
They said money was needed to provide relief items like tents, blankets and plastic sheets.
Pakistan's army is engaged in a fierce campaign against militants in the north-west of the country.
Attempts by the government in Islamabad to negotiate with militants in areas along the border with Afghanistan appear to have failed, correspondents say.
The country has been hit by a spate of recent suicide bombings widely blamed on militants - including a devastating attack this month on the Marriott hotel in Islamabad.
The bombing killed more than 50 people, most of them Pakistanis.
Militants use the tribal areas as a base for operations in Pakistan and across the border in Afghanistan.
The Taleban and al-Qaeda are believed to operate in these border areas after being pushed out of Afghanistan.
Their presence in the border regions have prompted a number of US attacks inside Pakistan.
Those attacks have angered Pakistan's government, and there have been incidents around the border involving Pakistani troops firing warning shots at US helicopters.