In taped comments on Aljazeera television, a spokesman identified as Abd al-Latif Hakimi said on Friday that the Taliban's leader Mullah Muhammad Umar is safe.
"We will carry out more attacks against international coalition forces if they continue to chase us," said Hakimi.
US-led forces ousted the Taliban in 2001 following the September 11 attacks in Washington and New York city.
Pakistani troops and US-led forces in Afghanistan have launched new offensives on either side on the border in remote and mountainous areas in an effort to kill or capture Taliban and al-Qaida leaders, including Usama bin Ladin.
"The Pakistan government launched operations against us.
Therefore we will launch operations against them. They closed the border between Afghanistan and Pakistan, so how can they say that the Taliban are crossing over?" said the spokesman.
"We will attack the American forces on these borders," he
More soldiers killed
Earlier, Pakistani government officials said 15 soldiers were killed in heavy fighting with a group of fighters, possibly including a top al-Qaida member, on the Afghan border.
Pakistani troops resumed their offensive against a cornered group of fighters, possibly including Usama bin Ladin's second-in-command, after the expiry of a noon (07:00 GMT) deadline for them to surrender.
"The operation is on," said military spokesman Major-General Shaukat Sultan, although he did not refer to the deadline that another officer had earlier said had been set for the group to give up. Sultan declined further comment.
Pakistani troops have faced fierce resistance from suspected al-Qaida fighters and tribesmen in the South Waziristan area since launching a sweep on Tuesday, leading to speculation they may be protecting Ayman al-Zawahri, bin Ladin's right-hand man.
Al-Zawahri (R) is bin Ladin's
number 2 man
A resident in Wana town, near the scene of the battle, said there had been two loud explosions as three helicopters hovered over the area soon after the deadline passed. Small-arms fire could also be heard, he said.
The fighting is centred on an area to the west of Wana that includes the village of Shin Warsak.
Al-Zawahri, an Egyptian doctor, is regarded as the brains of al Qaida and believed to be one of the key figures behind the 11 September, 2001, attacks on the United States.
The capture of one of the world's most wanted men would be a major coup for the United States, under fire over its rationale for the war in Iraq as the first anniversary of the start of that conflict approaches on Saturday.
Boost for Bush
It would also be a boost to George Bush ahead of this year's presidential elections, in which security is a major theme.
An intelligence official said al-Zawahri might be among a group of rebels who tried to flee the Pakistani offensive on Tuesday and who took refuge in Shin Warsak village.
The fighters' vehicle had come under fire and there was speculation some of those inside, perhaps al-Zawahri, might have been wounded, the official said.
Former Taliban official: unlikely
bin Ladin, al-Zawahri cornered
Western intelligence sources say al-Zawahri and bin Ladin were believed to be close to each other, somewhere in Pakistan's Waziristan. One Pakistani official said bin Ladin was not among the fighters in the compounds but did not explain how he knew this.
Pakistan President Pervez Musharraf told CNN on Thursday that the ferocity of the resistance his forces had encountered led generals to believe they were shielding an important militant.
Prospects of catching a senior al-Qaida leader have come to nought several times in the past, but given the ferocity of the ongoing battle, analysts say at the very least some senior militants could be among the defenders.
No Pakistani officials have said for certain that al-Zawahri was in the compounds under attack.
But an official of Afghanistan's ousted Taliban government said on Friday he doubted al-Zawahri was among the cornered militants.
"According to my information Dr Ayman al-Zawahri is not in that area," said former Taliban defence minister, Mullah Obaid Allah Akhund.
"It would be speculation to say where senior al-Qaida leaders have taken shelter because they keep on changing their hideouts," said Akhund.
A Pakistan army officer said government forces had arrested 26 suspected fighters, many of whom appeared to be foreigners from central Asia, since Thursday.