The Pakistani army is meeting heavy resistance as it continues its attacks on positions held by Islamic militants close to the Afghan border.
The fighting around Wana has been fierce
Thousands of soldiers have been involved in fierce clashes with hundreds of fighters - both sides are using heavy artillery and mortars.
Some reports suggest al-Qaeda's number two, Ayman al-Zawahri, is surrounded.
However senior Pakistani officials have not confirmed this, and officials in Washington are urging caution.
The fighting is taking place near the town of Wana in remote South Waziristan region.
BBC correspondents in Islamabad say there have been casualties on both sides, but precise figures remain unclear.
Locals say helicopter gunships went into action from day break on Friday, firing rockets and machine gun rounds at several fortified compounds where al-Qaeda suspects and local tribesmen were thought to be holed up.
Troops have thrown a wide cordon around the combat area and are gradually closing in. Hundreds of troop reinforcements are also being sent to the unruly tribal area.
Tribal leaders have appealed for a ceasefire, but to no avail.
The Pakistani army has denied reports from local civilian officials that the militants had been given a deadline of noon (0700 GMT) to surrender.
"The militants... appear to be determined to fight until the end," military spokesman Major-General Shaukat Sultan told the AFP news agency.
Many people have fled the area because of the fighting.
US and Afghan forces are said to have strengthened positions on the Afghan border to try to prevent al-Qaeda fighters escaping from the Pakistan offensive in South Waziristan.
US reconnaissance aircraft, including Predator drones and U2 spy planes, have been used over South Waziristan, liaising with the Pakistani forces, according to US military officials.
On Thursday Pakistani President Pervez Musharraf said his troops appeared to have ringed a "high-value target" after fierce resistance.
However he would not be drawn on who it might be.
US Deputy Defence Secretary Paul Wolfowitz said the possible capture of Mr Zawahri would be "huge".
But he urged Americans not to get obsessed with the "silver bullet solution".
"Obviously getting [Osama] Bin Laden would be a very big thing," he said.
"But anyone who thinks that's going to be the end of al-Qaeda, or the end of these terrorist networks, doesn't understand how they work," he added.
The United States has offered a $25m reward for information leading to Mr Zawahri's capture.
On Thursday, the US House of Representatives doubled the reward on Bin Laden to $50m.
BBC security correspondent Frank Gardner says the area being surrounded is 25 square kilometres (10 square miles) and there is a chance the militants could slip away.
If Mr Zawahri was captured, he adds, it would be a major blow to the militant network founded by Bin Laden.
Egyptian in origin, Mr Zawahri is believed to serve as Bin Laden's spiritual adviser and doctor. He is also the architect of the al-Qaeda ideology.
In 1998, he was the second of five signatories to Bin Laden's "fatwa" calling for attacks against US troops and civilians.
He was a key figure in the Egyptian Islamic Jihad group, which later merged with al-Qaeda.
Mr Zawahri has appeared alongside Bin Laden in al-Qaeda videotapes released since the 11 September 2001 attacks in the US.
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.
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.
Fifteen Pakistani soldiers died there in clashes on Tuesday and 24 militants, thought to be local tribesmen or al-Qaeda suspects, were also killed, Pakistan's army said.
The operation coincided with the arrival in Islamabad of US Secretary of State Colin Powell for meetings with the Pakistani leadership.