Nearly 4,000 families have fled Pakistan's Bajur tribal agency into Afghanistan's Kunar province, the U.N. High Commissioner for Refugees said in a statement.
Bajur is the most northerly of Pakistan's wild tribal regions, several of which have fallen largely under the control of militants opposed to the Afghan and Pakistani governments.
According to Pakistani officials, the fighting in Bajur has displaced as many as 500,000 people. Most have found shelter with relatives across northwestern Pakistan, though about 100,000 have taken refuge in camps set up by Pakistani authorities.
Pakistan's army claims to have killed more than 1,000 militants in the two-month-old offensive in Bajur. It has declined to estimate casualties among civilians.
Pakistan's border region is considered a likely hiding place for al Qaeda leader Osama bin Laden.
"In the last two weeks alone, over 600 Pakistani families have fled into Afghanistan," the UNHCR said. "While the vast majority of them are living with their relatives and friends, there are already some 200 families who live in the open air."
The UNHCR said it believes the majority of those who have crossed into Afghanistan will return home once the fighting stops.
U.S. officials have praised the operation in Bajur, which Pakistan's army says has been serving as a sanctuary for insurgents fighting on both sides of the border.
Militants use Pakistan's tribal areas as a base for their operations inside Pakistan but also for cross-border attacks in Afghanistan. The number of attacks along the border with Pakistan in eastern Afghanistan has gone up by 30 percent this year compared with 2007.
Maj. Gen. Jeffrey Schloesser, the top U.S. commander in eastern Afghanistan, which borders Bajur, told The Associated Press last week he was encouraged by Pakistan's offensive, but hadn't yet seen a drop in the number of militants crossing the border.
"We need a persistent series of operations by Pakistan over a lengthier period of time before we see a change there," Schloesser said.
The existence of sanctuaries in Pakistan, and the ability of Taliban and al Qaeda fighters to reconstitute there after they were pushed out of Afghanistan in 2001, has prompted a number of U.S. attacks inside Pakistan.
A raid by American commandos into Pakistan's South Waziristan tribal areas on Sept. 3 angered many in Pakistan.