Alliance forces are pushing al-Qaeda fighters back
The commander of the US military in Afghanistan, General Tommy Franks, said many al-Qaeda fighters had been killed or captured and steady progress was being made.
A local Afghan commander has said that up to 300 Taleban and al-Qaeda fighters may be ready to surrender.
But a BBC correspondent at Tora Bora says that so far there is no sign of that happening.
On Saturday, two US B-52s dropped powerful bombs on the mountain range, witnesses said.
Defence Secretary Donald Rumsfeld said the allied forces had advanced about two kilometres (1.25 miles) during the past eight hours in what he called fierce fighting.
Speaking to reporters en route to Central Asia, he also said 50 al-Qaeda fighters had surrendered and that they were running out of escape routes.
Overnight raids
The Pentagon believes between 300 and 1,000 of Osama Bin Laden's al-Qaeda loyalists remain in Tora Bora, trapped within two valleys.
To the south, Pakistani troops are helping to patrol the border with Afghanistan. But General Franks conceded it was possible that Bin Laden might have fled Tora Bora and escaped into Pakistan.
A local Afghan commander, Hazrat Ali, said al-Qaeda fighters were being driven from their caves to higher ground as the land and air assault continued.
In other developments:
Speaking at US Central Command in Florida, General Franks could not confirm reports that two American soldiers had been injured.
But he did confirm that an American man captured with Taleban forces at Mazar-e-Sharif had been moved out of Afghanistan.
John Walker is being detained on board the warship USS Peleliu in the Arabian Sea while the American authorities decide what to do with him.
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If al-Qaeda leaders are taken prisoner, they too might be moved to US warships.
General Franks said they could also be detained at Kandahar airport, which is now under the control of the US marines.
The Pakistan-based Afghan Islamic Press Agency reported that Bin Laden had left Tora Bora 10 days ago before the bombardment began.
The BBC's Damian Grammaticas, who is in the area, said B-52 sorties over Tora Bora came every 20 minutes, hurling plumes of ash and dust skywards.
An Afghan commander, Adji Moussa, said his men had captured between six and eight new caves from the al-Qaeda forces.
They found heavy weapons, ammunition and more video cassettes, but no sign of Bin Laden.
US officials say the ferocity of the al-Qaeda resistance and reported sightings of Bin Laden indicated his presence, but Mr Rumsfeld has conceded they could not be certain he was still in Afghanistan.
"I have seen reports that people believe are from reasonably reliable sources that in one case suggest he's still in Afghanistan, in another case suggest he's out of Afghanistan," Mr Rumsfeld said.
The US defence secretary is due to visit Azerbaijan, Armenia and Georgia in the Caucasus before going on to Uzbekistan in Central Asia on Sunday.