Earlier, IS released an audio recording, saying its signature black flag was flying over the hulking mountain range. The message was broadcast on the militants' Radio Khilafat station in the Pashto language late yesterday.
It also said IS has taken over several districts and urged villagers who fled the fighting to return to their homes and stay indoors.
The Tora Bora mountains hide a warren of caves in which al-Qaeda militants led by bin Laden hid from US coalition forces in 2001, after the Taliban fled Kabul and before he fled to neighbouring Pakistan.
According to testimony from al-Qaeda captives in the US prison at Guantamo Bay, Cuba, bin Laden fled from Tora Bora first to Afghanistan's northeastern Kunar province, before crossing the border into Pakistan. He was killed in a 2011 raid by US Navy SEALs on his hideout in the Pakistani garrison town of Abbottabad.
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Pakistan denies such charges, pointing to senior al-Qaida operatives it has turned over to the United States.
Meanwhile, Taliban spokesman Zabiullah Mujahid told The Associated Press in a telephone interview that Taliban fighters pushed back the Islamic State group from areas of Tora Bora that IS had earlier captured.
Mujahid claimed that more than 30 IS fighters were killed in battle. He also added that a US airstrike on Taliban positions yesterday that killed 11 of its fighters had benefited the Islamic State group.
Afghan officials earlier said that fighting between IS and the Taliban, who had controlled Tora Bora, began on Tuesday but couldn't confirm its capture.
Afghan Defense Ministry's spokesman Daulat Waziri would not say whether IS was in complete control of Tora Bora. But he said Afghan forces engaged IS militants in the Chapahar district of eastern Nagarhar province, killing five and pushing them out of the area.
The province, which borders Pakistan, is the main foothold of the Islamic State group in Afghanistan. An affiliate of the IS, which is fighting in Syria and Iraq, emerged over the past two years and seized territory, mainly in Nangarhar.
While the United States estimates there are about 800 IS fighters in Afghanistan, mostly restricted to Nangarhar, other estimates say their ranks also include thousands of battle- hardened Uzbek militants.
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