The killing of Ahmed Wali Karzai, the most powerful Afghan in the south of the country, will reinforce the feeling among Afghans that the Taliban can strike anywhere at any time and are not weakening as American military commanders have claimed.

This will be the impact regardless of who killed Mr Karzai because the assassination follows the attack on the Intercontinental Hotel in Kabul and the killing of top officials in northern Afghanistan.

These spectacular and highly publicised attacks are typical of developments in the war since the United States launched its troop surge in 2009, which is now in the process of being reversed. The Taliban reportedly killed and wounded 56 per cent more US soldiers in the nine months leading up to May, compared with a similar period a year earlier. When they have come under pressure in one valley, they move to another one.

If necessary, they can also take temporary refuge in Pakistan, which shares a 1,550-mile border with Afghanistan – about the same distance from London to Moscow. Also in the Taliban's favour is the deteriorating relationship between the US and Pakistan since the killing of Osama bin Laden.

There are other signs the Taliban remain a well-organised military group, such as the spectacular escape from Kandahar prison of 541 prisoners down a 1,200ft tunnel dug over five months in April this year. The US claim to have killed many mid-level Taliban commanders is probably true, but they are being replaced by vengeful cousins and brothers who are less likely to support local or national peace agreements than their predecessors.

The overall problems of the Afghan government and its foreign allies remain the same. The central government is weak and is regarded as a collection of racketeers by much of the population. The Taliban may not be very popular, but the total alienation of so many Afghans from the government gives it undiminished political and military strength.

Claims of social and economic progress are also often misleading. More children may go to school and university but there are few jobs for them when they graduate. Despite the US spending $10bn (£6bn) a month, millions of Afghans try to survive on $2 a day.