The orders were given several days in advance of Monday's arrest in Pakistan of Zaki ur Rehman Lakhvi, a senior LeT commander, suspected by Indian officials of assisting the planning of the Mumbai attacks.
The arrest, which a senior Pakistani intelligence official confirmed to CBS News, came as part of a series of raids by Pakistani forces on camps used by Lashkar-e-Taiba.
According to information shared with CBS News on the LeT's orders, a number of the group's militant warriors were already holed up in Pakistan's tribal areas which lie along the country's border with Afghanistan -- a territory where the Pakistani military is fighting Islamic militant groups.
The tribal area has become the militants' focal point. Al Qaeda and the Taliban, through support from groups such as LeT, are waging a resistance movement against the Pakistani military on the Pakistani side of the border and against U.S. and NATO troops on the Afghan side of the border.
A senior security official from the Middle East with access to information on LeT's workings said that most of the group's militant fighters were in the tribal areas when the Mumbai attacks took place.
These militants had apparently moved out of the Pakistani portion of Kashmir between early October and mid-November, ahead of snowfall in the region, which makes it practically impossible for them to cross the mountainous snow-clad passes between the Pakistani side of Kashmir and the Indian portion of Kashmir.
"You have to know a bit about the tactics of this group before you understand what they are doing right now," said the Middle Eastern security official, who spoke to CBS News on condition of anonymity. "I know on good authority that Lashkar-e-Taiba during the past few days has ordered its people to leave from the tribal areas for Afghanistan."
A Pakistani security official, familiar with the investigations ahead of Monday's arrest of Lakhvi, speaking to CBS News on condition of anonymity said, "Most of these militants had either left for Afghanistan or were in the process of leaving from the tribal areas."
The Middle Eastern security official said the implication of the LeT's move may be that the group will now try to retaliate against Pakistan's military forces by staging a larger number of attacks after regrouping on Afghan soil.
"The possibility of more attacks on Pakistan by LeT members cannot be discounted" he said.
Pakistan's government has ordered a tightening of security at mosques and other places of worship ahead of Tuesday's Eid-ul-Adha festival, which follows the Hajj, an annual Islamic pilgrimage to Mecca. This year, the height of the Islamic festive season comes as government forces wage a new crackdown on militants.