Pakistani forces say they have surrounded up to 400 heavily-armed militants near the Afghan border and are closing in on them.
The fighting around Wana is described as fierce
A military spokesman said at least two of the fighters had died attempting to break the cordon on Friday.
There is speculation that a senior al-Qaeda leader, possibly Osama Bin Laden's deputy Ayman al-Zawahri, is among those cornered.
But Pakistani and US officials are playing this down.
Thousands of Pakistani army and paramilitary troops, backed by an artillery and aerial bombardment, are involved in the operation near the town of Wana in South Waziristan tribal region.
They are said to have thrown a cordon 10 kilometres by five kilometres (six miles by three miles) around the militants - believed to be foreign Islamic fighters, Afghan Taleban and their Pakistani tribal allies - who are putting up fierce resistance.
Their efforts are being supported by US-led forces on the Afghan side of the border.
Pakistan's military spokesman, Major General Shaukat Sultan, said an estimated 300 to 400 fighters were within the cordon, adding: "This is an assessment from the fire we are receiving."
He described the fighters as "well dug-in" and ready "to fight until the end".
General Sultan said the two fighters who died were in a group of 10 that tried to break through Pakistani lines. They were later identified as a Chechen and an Arab national.
He added that details of the casualties suffered by Pakistani forces would be given once the operation was over.
At least 15 soldiers died in day one of the operation on Tuesday. The army says 24 militants, thought to be local tribesmen or al-Qaeda suspects, were also killed.
Correspondents say there have been further casualties on both sides since then, but precise figures remain unclear. No journalists have been allowed into the area.
General Sultan disputed claims by Pakistani officials
that captured militants had revealed that Egyptian-born Zawahri - who has a $25m American bounty on his head - was among those cornered, and possibly injured.
"So far, whatever people we have apprehended, we have not
got confirmation from them," he told journalists.
However, he added: "The type of resistance, the type of preparation of their
defensive positions, the hardened fortresses they have made
means we can assume that there could probably be some
high-value target there."
A spokesman for the Taleban has reportedly warned that it will attack US and Pakistani forces if they
do not halt the operation.
"We will carry out more attacks against international
coalition forces if they continue to chase us," the spokesman was quoted as saying in taped comments translated into Arabic by al-Jazeera television.
US President George W Bush's National Security Adviser, Condoleezza Rice, said: "There clearly is a fierce battle going on there on the Pakistani-Afghan border.
"But I think we don't know whether there's a high-value target there, and we certainly don't know whether it's al-Zawahri. We'll just have to wait and see."
On Thursday, the US House of Representatives doubled the reward on Bin Laden to $50m.
'Hammer and anvil'
US-led forces in Afghanistan have stepped up operations in areas near the border with Pakistan as part of a major anti-militant operation across southern and eastern Afghanistan codenamed Mountain Storm.
They aim to create a "hammer
and anvil" effect with Pakistani forces, to ensure no militants
can escape by simply crossing the border.
US military spokesman Lieutenant-Colonel Bryan Hilferty
said more than a dozen militant suspects had been detained in
the past week in Khost region, to the north-east of
the Pakistani operation.
But he also said there was no indication they
included any senior figure.
The Pakistani operation is being described as the biggest since the hunt for Bin Laden and his associates started in the area more than two years ago.
Its start coincided with the arrival in Islamabad of US Secretary of State Colin Powell for meetings with the Pakistani leadership.
South Waziristan with its mass of mountains and hills has been cited many times as the most likely hideout of Bin Laden and al-Qaeda elements.