JALALABAD - When Afghan troops pushed into Kot, a district close to the border with Pakistan, this week, they found many of the houses empty, with posters plastered on the walls and black flags left by departing Islamic State fighters.

Backed by US special forces troops and airstrikes that authorities say have killed hundreds of Islamic State fighters in recent weeks, the Afghan army has launched an offensive against the movement, which is now believed to be confined to three or four districts in eastern Afghanistan.

Afghan commanders said they faced little resistance as they pushed into Kot after a heavy air and artillery bombardment as fighters pulled out into nearby mountain areas. "We have already destroyed their training camps in Kot district and the operations will expand to other districts too," said Shereen Agha, an Afghan army spokesman.

Provincial government spokesman Attahullah Khogyani said 78 Daesh fighters had been killed in the operation and many bodies had been concealed inside houses to hide the number of fatalities they had suffered. Five US special forces troops, fighting alongside Afghan special forces, were injured in the fighting.

Involving both regular army and special forces, the operation in Nangarhar, dubbed "Wrath of the Storm", coincided with last week's suicide bombing in Kabul that killed at least 80 people and wounded more than 230 more.

The operation, the Afghan army's first major strategic offensive of the summer, was planned well before the attack on a demonstration by mainly Shi'ite Hazara people in Kabul. But that attack, which was immediately claimed by Islamic State, added urgency to the operation, which military officials say has pushed Daesh fighters back into the mountains of southern Nangarhar.

Abdul Hakim, one of the residents left in the dusty town bazaar, gave a careful welcome to the incoming troops. "I am very happy to see the government forces defeated Daesh and saved us from the atrocities and terror," he said as troops moved about pulling down the posters and flags covering many of the surrounding walls.

However after innumerable false dawns in decades of conflcit in Afghanistan, officials in the NATO-led coalition that provides assistance to Afghan forces are cautious about declaring success against Islamic State, which President Ashraf Ghani promised to "bury" in January.

According to figures quoted in a report by the Special Investigator for Afghanistan, a US watchdog, Afghan government forces control just under two thirds of the country, 5 percent less than at the start of the year.

But Western officials say the army has increasingly taken the offensive against the insurgents, both Taliban and Islamic State, and prevented the fall of district and provincial centres.

Previously considered a much smaller threat than the Taliban, their bitter enemies, the Kabul bombing underlined how dangerous they could be, even without holding large tracts of territory.

Afghan and US military officials believe the concentrated attacks on the movement over the past six months have killed many of its fighters and leaders and weakened the group, despite its ability to mount the Kabul attack.

Gen. John Nicholson, the senior US commander in Afghanistan, said this week that the number of Daesh fighters, estimated at around 3,000 in January, has been roughly cut in half and now stood at between 1,000-1,500.