Kashmir-born Jilani, who was recently acquitted over involvement in the 13 December 2001 attack on the Indian parliament which left nine people dead, survived the shooting.
He is currently in intensive care and recovering well. Doctors said he has not yet given a statement to police.
Delhi's police commissioner, KK Paul, said delays in informing the police about the shooting incident were the cause of a lack of evidence.
"The police were informed about the attack almost 45 minutes to one hour after it occurred. There was a long delay. If this had not been so, we would have been able to find more evidence," he said on Friday.
Paul did not comment on the investigation, adding: "The investigation is on and it is not right to comment before getting the report."
Jilani's lawyer Nandita Haksar, however, said police claims that there was a delay in reporting Jilani's shooting are a "blatant lie".
A high court cleared Jilani of the
parliament attack that killed nine
"This is absolutely incorrect," she said. "He was taken in as a medical registered case and the police knew about it the minute he was registered."
She says she took Jilani to Delhi's All India Institute of Medical Sciences hospital after he was shot outside her home at Vasant Enclave, an upmarket residential area in south Delhi, on Tuesday evening.
She said the police were either unable to locate evidence or were unwilling to do so.
After the shooting, Haksar said she believed Jilani was being followed or someone had listened to their telephone conversation before his arrival at her house that evening to seek legal advice.
She beleives the Delhi police and the Indian intelligence bureau are harassing Jilani after his acquittal over the Indian parliament attack.
Relatives accuse security
In Indian-administered Kashmir, Jilani's relatives, supporters and students at Delhi University's Zakir Hussain College have accused the special cell of Delhi police of orchestrating the assault. They believe the cell is now dragging its feet in the investigation for obvious reasons.
A prominent Kashmiri separatist leader, Sayid Ali Shah Jilani, described the attempt on Jilani's life as an act of "state terrorism".
Meanwhile, Kashmir's pro-independence Jammu Kashmir Liberation Front (JKLF) chief, Muhammad Yasin Malik, said the Armed Forces Special Power Act and similarly draconian laws in force in the Himalayan state had been extended to other parts of India.
"The shooting of Jilani is a glaring example," he said at a JKLF meeting to commemorate the execution of its co-founder Maqbool Butt.
On Thursday, Indian Home Minister Shivraj Patil said the government could hand over the investigation to the country's premier investigation agency, the Central Bureau of Investigation (CBI), if necessary.
"We are not averse to the Jilani probe being handed over to the CBI. We will do whatever the court directs," Patil said.
The move is seen as a setback to the special cell of the Delhi police.
Manmohan Singh is said to have
asked for a report on the case
The investigation has been entrusted to the crime branch partly because the special cell, designed to tackle terrorism-related crimes, had been entrusted with the parliament attack case and had claimed Jilani was a prime suspect.
Although a special anti-terrorist court had sentenced Jilani to death, the Delhi high court later cleared him. Delhi police challenged Jilani's acquittal in the Supreme Court in December 2003.
Indian Prime Minister Manmohan Singh and Home Minister Patil have sought a case update from Paul.
Delhi police claim the handover is routine. But Indian newspaper The Asian Age, quoting official sources, reported on Friday that it was media pressure and public opinion that prompted it.
Indian soldiers in a raid to catch
those who attacked parliament
It also said that sources admitted the special cell had sometimes inappropriately deviated from its task of tackling terrorism, although standing orders gave them a free hand in other crime cases.
One unnamed police official was quoted as saying: "There have been occasions when cases vested with other branches of the Delhi police were cracked by the special cell, much to their credit."
In the process, some special cell officials crossed departmental boundaries by taking on other cases.
The Indian government has also formed a medical board to investigate the shooting.
"The panel was formed to examine several key questions that remain unanswered about the attack on Jilani," official sources said.
The board will look into the nature of Jilani's injuries, the direction from which the bullets were fired and whether the shots came from one or more pistols.
"The panel was formed to examine several key questions that remain unanswered about the attack on Jilani"
Police are preparing a list of people who visited Shaukat Hussain Guru and Muhammad Afzal, the two others convicted of the attack on parliament, in jail during the past six months as part of the investigation into the shooting. Both Hussian and Afzal also come from Baramulla, Jilani's home town.
The highest Indian court has sought a report on Tuesday's shooting.