An estimated 20,000 tribesmen crowded into Khar, six miles from the school that was shredded by air strikes on Monday. Cries of "Down with America" rang out as radical clerics addressed the turbaned protesters, many of whom brandished Kalashnikovs or rocket launchers.

"Our jihad will continue, God willing," thundered Maulana Faqir Muhammad, a firebrand preacher with links to al-Qaida. "And our people will go to Afghanistan to oust American and British forces."

Inayat ur Rehman claimed to have a "squad of suicide bombers" waiting to kill Pakistani soldiers, imitating Iraqi attacks on Americans. When he asked if the crowd would support the measure, the tribesmen replied with a unison "Yes".

The protesters claimed that Monday's strike in Chingai village had killed innocent religious students, not international terrorists. But the Pakistani government insisted the school was a front for an al Qaida meeting facility.

One official, speaking on condition of anonymity, said the madrasa had frequently been visited by Osama bin Laden's deputy, Ayman al-Zawahiri, and by Abu Ubaidah al-Masri, an Egyptian militant who is suspected to have masterminded last summer's alleged plot to bomb trans-Atlantic airliners.

But he said neither was at the madrasa at the time of Monday's attack, Associated Press reported.

The Khar rally was the largest of several across North West Frontier, Sindh and Punjab provinces, where American flags and effigies of George Bush were burned.

Samina Ahmed of the Crisis Group thinktank said the strike was counterproductive and would spell "big trouble" for Pakistan and the US. "An attack on a madrasa in which 80-something people are killed is great propaganda for the Taliban," she said. "This will inflame opinion among Pashtuns on both sides of the border and boost recruitment."

Tensions were increased by widespread suspicions of US involvement in the attack. Last January, a pilotless Predator drone struck at a house just two miles from the Bajaur madrasa, killing 18 people but missing its target, al Zawahiri.

America's role in the latest strike is unclear. President Pervez insisted that his solders were solely responsible, an assertion supported by the US military in Afghanistan. "I can assure you without doubt that [we] had nothing to do with that attack," said spokesman Colonel Tom Collins.

Pakistan's chief military spokesman, Major General Shaukat Sultan, said the US provided intelligence that led to the strike - a statement he later tried to withdraw. But he refused to deny US involvement.

"Intelligence comes from 101 different sources - media reports, satellite photos, agents, many sources. I can't pinpoint a source on this particular operation," he told the Guardian.

Doubts over the official explanation were fuelled by measures limiting media access to the site of the attack. Soldiers prevented local journalists from reaching Bajaur, while foreign correspondents were barred from the tribal areas. The timing of the attack also roused suspicions. Just days earlier, President Musharraf's officials were talking peace with the Bajaur militants and had freed several prominent fighters as a gesture of goodwill. The two sides were due to sign a deal yesterday.

Instead, the military bombed the school and killed Maulana Liaqatullah, one of the radical clerics with whom the government had been negotiating, and badly inflamed anti-government hostility across the province. Islamist clerics and politicians said they were convinced America had spurred the attack.

Sahibzada Haroon, an MP for the Jamaat Islami party, who lives nearby, said he heard two large explosions "so powerful they shook the earth and rattled our doors and windows" early Monday morning. Fifteen minutes later Pakistani army helicopters arrived, fired a handful of rockets and left.

"Those were small thuds - nothing in comparison to the big explosions that preceded them minutes earlier," Mr Haroon told Dawn newspaper. "I have no doubt in my mind that it was done by the Americans and we are now making a futile attempt to cover it up."

Lying in a hospital bed in nearby Peshawar, Abu Bakar, one of just three seminarians to survive the strike, insisted the madrasa was engaged in education and not terrorism. "We had come to learn Allah's religion," said the 22-year-old, whose legs were broken by falling rubble.

Human Rights Watch said the strike raised questions about Pakistan's "persistent use of excessive and disproportionate force in pursuing counter-terror operations".

Ms Ahmed predicted that the strike would spell further upheaval in the tribal areas. "This doesn't help anybody's cause except the Taliban's," she said.