THE discovery of three American soldiers among the dead in a suicide bombing at the opening of a girls’ school in the northwestern Pakistan town of Dir last week reignited the fears of many Pakistanis that Washington was set on invading their country.

Barack Obama has banned the Bush-era term “war on terror” and dithered about sending extra troops to Afghanistan, but across the border in Pakistan, the US president has dramatically stepped up the covert war against Islamic extremists.

US airstrikes in Pakistan, launched from unmanned drones, are now averaging three a week, triple the number last year. “We're quietly seeing a geographical shift,” an intelligence officer said.

For the past month drones have pounded the tribal region of North Waziristan in apparent retaliation for the murder of seven CIA officers in Afghanistan by a Jordanian suicide bomber working with the Pakistani Taliban.

Last week America launched its first multiple drone attack, according to Pakistani security officials. Eighteen missiles were fired from eight unmanned aircraft in Dattakhel village, killing 16 people.

The discovery of the dead US soldiers revealed that America’s shadowy war in Pakistan not only involves drones but also small cadres of special operations soldiers.

Pakistan’s foreign minister, Shah Mehmood Qureshi, insisted that US troops were in Pakistan only to provide counter-insurgency training for the Frontier Corps, a paramilitary force operating in the tribal areas.

Other sources said there were about 200 US military inside the country. “I’m not sure you could just call it training,” one official said. “They are hardly behind the wire if they are on trips to schools in Dir.”

The three US soldiers, who have been described variously as special operations forces and civil affairs troops, were killed when their convoy was bombed as it travelled to the re-opening of the school. It had been rebuilt with US aid after being bombed by the Taliban last year.

Three schoolgirls, two villagers and a Pakistani soldier were also killed in the attack, for which the Pakistani Taliban claimed responsibility. More than 100 were wounded, mostly schoolgirls.

It was officially reported that the device was a remote-controlled bomb. It has now emerged that a suicide bomber rammed into the vehicle carrying the Americans. This suggests the bomber had inside information. “This attack was too perfect: they lay in wait for the convoy to pass and knew exactly which vehicle to hit,” a US military officer told The Long War Journal.

One of those killed was Sergeant Matthew Sluss-Tiller, 35, the father of a three-year-old daughter. His mother, Jane Blankenship, said her son had been in Pakistan on a civil affairs mission and had grown a beard for it.

One official suggested the “trainers” may be used to pick up intelligence on drone targets, particularly because the CIA did not trust its counterparts from the ISI, the Pakistani intelligence service that has close links to the Taliban.

The Americans insist the drone attacks have been a success, picking off the second and third tier of Al-Qaeda’s leadership. In August they killed Baitullah Mehsud, leader of the Pakistani Taliban. They recently claimed to have killed his successor, Hakimullah Mehsud, but Pakistan’s foreign minister said this had not been confirmed.

To the irritation of Washington, Islamabad has kept up a pretence that drone attacks are carried out without its approval, even though the aircraft are based in Pakistan.

Among the Pakistani public, there has been outcry at the attacks. Surveys constantly show that Pakistanis consider the US a greater threat than the Taliban, despite 3,021 Pakistani deaths in terrorist attacks last year.

If the drones are controversial, the presence of US soldiers on Pakistani soil is far more so. Despite a $1.5 billion (£959m) aid programme, Robert Gates, the US defence secretary, had to fly into Pakistan two weeks ago to reassure its military leadership. “Let me say definitively the US does not covet a single inch of Pakistani soil,” he told Pakistan’s National Defence University.

Additional reporting: Daud Khattak