The battle is close to Tora Bora -- a part of Afghanistan that was the last known refuge of Al-Qaeda leader Osama bin Laden in late 2001.
The offensive at Tora Bora began with air strikes launched on August 14 by U.S.-led coalition aircraft.
Radio Free Afghanistan's corresponent Daud Wafa traveled to the Pacheragam district of Nangarhar Province, south of Jalalabad, to speak with some of those displaced by the fighting.
A villager forced from his home in the area, Allah Dad, tells Wafa that the coalition ground and air operations have been incessant.
"Planes are flying over during the night," Allah Dad says. "We can see the U.S. troops coming and going during the daylight hours."
Militants And Terrorists
Vanessa Bowman, a spokeswoman for U.S.-led coalition forces in Afghanistan, says the mountainous border region near the border with Pakistan has been an ideal environment for the Taliban and Al-Qaeda to conceal support bases and training sites.
Bowman says attacks aimed at terrorizing innocent civilians -- both inside and outside of the area -- have been planned and launched from the Tora Bora region of Nangarhar Province.
Afghan and U.S. troops also have been carrying out a ground assault on militants' positions -- which include labyrinths of cave complexes thought to have been used by bin Laden and hundreds of his fighters to flee into Pakistan in late 2001 or early 2002.
Thousands of Pakistani troops were deployed on Pakistan's side of the border this month to block escape routes for militants trying to flee from Afghanistan.
Afghan media have quoted local officials who claim hundreds of militants were killed during the first few days of the joint Afghan and international offensive.
But there has been no independent confirmation of casualty figures. U.S.-led coalition officials say they will not release details on casualties until after the operation has been concluded.
Fleeing The Area
Meanwhile, hundreds of villagers have been fleeing the fighting.
One elderly resident, Sayed Nabi, tells Radio Free Afghanistan correspondent Wafa that coalition forces have prevented civilians from traveling into the battle zone.
"The bombing has been going on for several days," Nabi says. "[Coalition forces] do not let people get close to the area [of the fighting]. And from our vantage point, we can't get further information about what is happening."
Another resident of the Pacheragam district, Mir Dad, says villagers fear attacks by Taliban as well as being mistakenly targeted by coalition air strikes.
"The operation has been going on at Tora Bora since [August 14]," Mir Dad tells Radio Free Afghanistan. "The [foreign] troops are coming and going, and the bombing has been severe. Civilians have been killed, too. [Residents] are afraid of both the Taliban and the Americans."
Nuragha Zwak, a spokesman for the governor of Nangarhar Province, confirms that some innocent civilians have been hurt by the fighting. But Zwak claims the Taliban and its sympathizers are exaggerating the extent of civilian casualties.
"Only three children have been injured. And because this operation is continuing, there is no exact information about casualties," Zwak says. "This information will be released as soon as the operation concludes. But [supporters of the Taliban] are spreading rumors of civilian deaths as propaganda."
A purported Taliban spokesman, speaking by telephone to Radio Free Afghanistan from an undisclosed location, has claimed that the Taliban shot down one coalition helicopter and destroyed at least two armored vehicles.
U.S.-led coalition officials have neither confirmed nor denied that report, saying they will not provide further information about the battle to the media until the operation is finished.
(Contributors to this report include RFE/RL's Radio Free Afghanistan correspondents Daud Wafa in Nangarhar Province and Mustafa Sarwar in Prague)