By David Loyn
BBC News, Delhi
Mr Qureshi had claimed 'consensus' in Pakistan to act against terrorist groups
Pakistan's reversal of a decision to send the head of its intelligence service to India is a political own goal, following the offer made by Prime Minister Yousuf Raza Gilani.
Mr Gilani, whose democratic government is the first in Pakistan for almost a decade, made the offer to show full co-operation with the Indian investigation.
But now a lower official from the Inter Services Agency (ISI) will come instead.
The decision damages Pakistan's case that all of the military organisations of the state are now under democratic control - a case put strongly in a BBC interview when their foreign minister Shah Mahmood Qureshi told me there was now "consensus" among all of the institutions of the state to act against terrorist groups.
By coincidence it was on Wednesday, hours before the Mumbai incident began, that the Pakistani government scrapped the political wing of the ISI.
The move aimed to reduce its political role, after the failure in July to take it out of the army's control and put it under the interior ministry.
In the past the ISI has had strong links with Islamist militant groups, going back to its (then US-funded) sponsorship of the Mujahideen against Russian control of Afghanistan in the 1980s, and backing for the Taleban in the 1990s.
While Pakistan now fights Taleban forces, it backed them in the 1990s
In the early 1990s, a campaign to end Indian control of Kashmir became far more violent, and the Lashkar-e-Toiba was among groups which benefited from Pakistani state support to train militants for that cause.
It was this group which trained the Mumbai militants for three months, according to a statement leaked to Indian newspapers, said to have been made by the one alleged militant captured alive, named as Azam Amir Qasab.
The Lashkar-e-Toiba was banned by the military-led government of Pakistan in 2002 at US insistence.
But it changed its name to the Jamaat-ud-Dawa and, after serving brief jail terms, its leaders emerged to continue to inspire jihad against Indian control of Kashmir.
Despite the Pakistani government's promise to end the activity of this group, several years later it continued "largely unabated", according to an investigation by the think tank International Crisis Group.
By 2007, when the military government did appear to be trying to crack down, it found itself victim to what analysts call "Islamic blowback" - attacks on itself by groups once favoured and now out of control.
In a remarkable series of interviews published in the New York Times, Carlotta Gall reported former ISI operatives admitting that parts of the agency were trying to stop attacks by militants that others in the same organisation were still financing.
One former senior intelligence official was quoted as saying, "We indoctrinated them and told them 'You will go to heaven'. You cannot turn it around so suddenly."
Apart from the leaked report about the one alleged militant said to have been taken alive this week, the only other concrete indication about the group who carried out the attacks on Mumbai was a statement by a previously unknown group, the "Deccan Mujahideen".
Indian PM Singh is under pressure to explain failures to prevent the attacks
A number of smaller attacks have been admitted by the "Indian Mujahideen" this year.
Indian police sources have been quoted as saying that this group was created by the ISI and formed from members of existing groups including the Lashkar-e-Toiba.
The Telegraph newspaper, based in Kolkata, reported that police were connecting the Indian Mujahideen with the "Students' Islamic Movement of India", who called the claim a "figment of the imagination" of the IB (Intelligence Bureau).
With state assembly elections currently under way, the Indian government is under pressure to explain the intelligence failures that led to such a carefully planned and audaciously executed attack.
That explains the unusually strong statement by Prime Minister Manmohan Singh on TV on Thursday threatening a "cost" to be paid by Pakistan if suitable measures were not taken.
After a recent gradual thaw, relations between these two hostile nuclear-armed neighbours look again to be on ice.