|Pakistan 'militant' group denies Osama Bin Laden link|
The phone was recovered during the 2 May US raid that killed both men.
Although banned there, analysts say HuM has links with Pakistani intelligence.
"Al-Qaeda had their own discipline, their own thinking, their own organisation. We have never ever been in touch with Osama," a spokesman for the group told the BBC.
The BBC's M Ilyas Khan says that it is difficult to establish if the group has had recent contact with al-Qaeda, but adds that it certainly has a long history of co-operation with al-Qaeda.
Our correspondent says the latest claims come at a time when Pakistan's military and intelligence services are under increasing pressure from the West, where there are suspicions that some elements of Pakistan's security establishment provide backing to militant groups and may even have helped protect Bin Laden.
This may be one reason why the group is denying any links with al-Qaeda, our correspondent says.
The report comes days after a Pakistani brigadier serving at the army's main headquarters was detained for allegedly having contacts with the banned extremist group Hizb-ut Tahrir. He denies the allegation.
Four majors in the Pakistani army were also questioned for involvement with banned militant organisations.
No 'smoking gun'
The New York Times report quotes unnamed senior US officials as saying that the contacts on the phone recovered from the compound indicate that Bin Laden used the group as part of his support network inside Pakistan.
It also said that US analysts had determined that HuM commanders had called Pakistani intelligence officials and one even said that they had met. However, they added, there was no indication that the contacts between Harkut ul-Mujahideen and Pakistani intelligence were anything to do with Bin Laden.
There was no "smoking gun" showing the spy agency was involved with protecting the al-Qaeda chief, the report says.
Nevertheless, US officials are treating the information as a "serious lead", according to one official quoted by the newspaper.
It also says the link may provide clues about Bin Laden's movement after he escaped US forces on the Afghan border nearly 10 years ago and why he eventually settled in Abbottabad, where he was killed. The paper says that the group has especially deep roots in the area around Abbottabad.
Indeed the group's former leader, Maulana Fazlur Rehman Khalil, is cited by the paper as being a co-signer of Bin Laden's 1998 edict ordering attacks against America.
It also adds that the group was central to organising press trips for journalists to see Bin Laden in Afghanistan before the 9/11 attacks.
Our correspondent, M Ilyas Khan, also says there is evidence to suggest that HuM has maintained links with the Pakistani intelligence service, the ISI.
Maulana Khalil, was called in by the military authorities to mediate in the government stand-off with militants occupying Islamabad's Red Mosque in 2007.
As recently as last year, HuM leaders were among several militant figures who were allowed to address public rallies in Pakistani-administered Kashmir to show solidarity with demonstrators in Indian-administered Kashmir, our correspondent says.