The army faces well-armed, well-trained militants in Waziristan
Unconfirmed reports say 50 more rebels died in fresh air strikes on Tuesday.
It is the heaviest fighting in the Waziristan region, which borders Afghanistan, for many months. Locals are reported to be fleeing the clashes.
US and Nato have been pressing Pakistan to do more to stop militants crossing the border to attack their troops.
The fighting is centred around the town of Mir Ali.
The bombing destroyed many shops and homes... We are leaving
Noor Hassan,
Mir Ali resident
Waziristan clash: Your views
Latest reports say many of its residents are trying to escape, but it is unclear how many are going.
One man interviewed by the BBC Urdu service on Tuesday morning who was among those leaving said that his nephew had been killed by army shelling.
The BBC's Barbara Plett in Islamabad says that Mir Ali is known as a base for foreign militants with links to the Taleban and al-Qaeda.
The violence has been escalating since mid-July when a ceasefire between the army and the militants broke down.
Access for journalists to the tribal areas is restricted and it is impossible to independently verify the casualty figures.
'Punitive action'
Military aircraft struck "one or two places" near Mir Ali on Tuesday, army spokesman Maj Gen Waheed, the Associated Press news agency reports. There were unconfirmed reports that about 50 militants had been killed.
As well as soldiers confirmed killed, the army says up to 15 soldiers who went missing on Monday are still unaccounted for.
The army says it has rejected a ceasefire proposed by the militants and will "continue punitive action till complete peace is restored", AP said.
Our correspondent says that, by all accounts, the fighting in North Waziristan has been extraordinarily fierce.
The army has been bombing suspected militant positions in villages using helicopter gun ships and jet fighters.
Locals report civilians among the dead, including women and children.
The battles are said to have begun when militants ambushed a number of army convoys on Saturday.
All changed
Traditionally the security forces kept out of the tribal border areas.
That all changed in 2001 after Gen Musharraf allied Pakistan to the US-led 'war on terror' and vowed to crack down on militants based in the tribal regions.
The militants want to overthrow Gen Musharraf
For much of that time there has been a heavy military presence in Waziristan.
But militants have still managed to increase their influence and control in many areas.
Hundreds of soldiers have been killed. But critics say that the military has not done enough to crack down on the militants.
Moreover, elements in the army and the intelligence services have been accused of helping them.
The military campaigns are deeply unpopular in Pakistan as they are widely seen as being carried out under American pressure.
Another batch of more than 200 soldiers were captured recently by militants, apparently without a fight.
The militants say they will kill them unless a number of prisoners are released and military deployment ends in their area.
So far, a number of the soldiers have been freed, while several others have been killed.
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The Pakistani army says that at least 150 to 200 Taliban militants, along with 50 Pakistani troops have been killed in  between al-Qaeda, Taliban fighters and Pakistani troops along the border region of Pakistan and Afghanistan in an area known as . At least 20 other troops were injured and at least 15 are reported to be missing. 12 civilians are also reported to have been killed.

"We have told them to surrender and give up their weapons," said Major General of the Pakistani army,  Waheed Arshad. Militants say that they are going to attempt to overthrow the government and take the newly elected Pakistani President Pervez Musharraf out of power.

The battles began on Saturday October 6 in the town of Mir Ali and have lasted three days so far. Army officials say that they will "continue punitive action until complete peace is restored." The battles were triggered after several Pakistani officials were targeted and peace talks with officials in Islamabad failed to go forward.

In September, Osama bin Laden issued a new audio tape in which he told militants to resist Pakistani troops and rebel against the army. He also asked militants to seek revenge for the assault on the Red Mosque when almost 100 were killed by militants and troops.