The exodus continued as Afghanistan's ruling Taleban put off making a decision on whether to hand over Osama Bin Laden.
Pakistani leaders have warned the Taleban's spiritual leader, Mullah Mohammad Omar, that unless he surrenders Bin Laden, a prime suspect in the destruction a week ago of the World Trade Center in New York, he risks a devastating US strike.
Aid officials are preparing themselves for the influx of refugees, moving tents, food supplies and staff to border areas.
But they are already overburdened with 2.5 million Afghan refugees, victims of civil war and drought.
Pakistan closed its borders on Monday as tens
of thousands of Afghans streamed toward the frontier.
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Thousands of refugees tried to cross into Pakistan at the border town of Torkham in northern Pakistan, but were turned away.
But much of the Afghan-Pakistan border lies in remote areas, and it is virtually impossible for the Pakistanis to prevent people coming in.
The UN says about 4,000 people have made the journey in the past two days, and it expects another 3-4,000 a day will continue to flood in. About 5,000 refugees are on the border near Kandahar, being prevented from crossing.
A BBC correspondent in Peshawar says most of the Afghans entering Pakistan are women and children; there are reports the Taleban is refusing to allow any men to leave in case they are needed to fight.
Kandahar - the principal city in the south and the headquarters of the Taleban - is reported by aid agencies to be half empty and Kabul a quarter empty.
UN spokeswoman Stephanie Bunker, said: "The situation is developing very rapidly right now.
"We are therefore prioritising assistance for the internally displaced people.
"We have to scale up assistance before winters that start in November."
The Taleban have refused to hand over the exiled Saudi-born militant Bin Laden, who has been living under their protection since 1996.
It would be a huge climbdown, but public endorsement by the clerics might make it possible.
Pakistan has already pledged to provide the US with support and, although the government will not spell out exactly what this means, Foreign Minister Abdul Sattar said he could not rule out the idea of basing foreign troops in Pakistan.
As the consultations went ahead, Reuters news agency quoted a Pakistani army captain as saying the Taleban had moved a large number of weapons, including missiles, to positions near the Pakistani border.
The Afghan rulers have warned that they might attack any country that offers assistance to the United States.
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Thousands have already crossed near the Pakistani city of Quetta, and the UN is now moving tents and food supplies to that area.
Nevertheless, a BBC correspondent says that the roads out of the capital Kabul and Jalalabad in the east are crammed with vehicles of people fleeing to the countryside.
The US is pointing the finger at me, but I categorically state that I have not done this
Osama Bin Laden
However there is still a possibility that the Taleban, fearing for their own regime, may hand him over.
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