The Taliban intends to "raise its voice for Muslims" in Indian-administered Kashmir, the BBC reports quoting a spokesman.
Suhail Shaheen told the BBC's Hindi service: "As Muslims, we also have a right to raise our voice for Muslims in Kashmir, India or any other country."
India and Pakistan control different parts of the Muslim-majority territory, but both claim it as wholly theirs, according to the report.
There has been violence on the Indian-run side for 30 years, because of a separatist insurgency, the BBC adds.
The Taliban have declared victory in Afghanistan following the withdrawal of US troops in August. The Islamists are now in control and expected to announce a new government, according to the report.
This is the first time the group has commented on Indian-administered Kashmir, the BBC report further says.
In an recent interview with CNN-News18 Taliban leader Anas Haqqani was quoted to have said: "Kashmir is not part of our jurisdiction and interference is against our policy."
In another interview with a Pakistan-based channel, Taliban spokesman Zabiullah Mujahid urged Pakistan and India to sit together to resolve all issues, according to the report.
Mr Shaheen was quoted to have told the BBC the Taliban "had no policy" of launching armed operations against any country.
His remarks come at a time when India has raised concerns about Afghanistan's Hindu and Sikh minorities under the Taliban, and there are rising concerns over what critics say is the rise in hate crimes against Muslims since 2014 under Prime Minister Narendra Modi's government, the BBC notes.
Two years after India revoked nearly all of Article 370 in the constitution, stripping Jammu and Kashmir of the autonomy it had been guaranteed, the valley continues to remain tense, the report says.
With Taliban in control of Afghanistan, many in India fear that sections within the group could now set their eyes on Indian-administered Jammu and Kashmir, egged on by anti-India elements within Pakistan, according to the report.
In a widely circulated TV debate clip, Pakistan's ruling PTI leader Neelam Irshad Sheikh was quoted as saying: "Taliban have said they are with us and they will help us in [liberating] Kashmir."
While countries like the US, Russia, China are openly talking with the Taliban, India is taking guarded steps, the BBC reports.
The Haqqani group has engineered and carried out attacks in the past against Indian assets, including the Indian embassy in Kabul, the report says citing Carnegie India report on India's Afghanistan strategy following the US withdrawal.
Mr Shaheen claimed the allegations against the Haqqanis are mere claims, according to the BBC report.
"The Haqqanis are not a group. They are part of the Islamic Emirate of Afghanistan. They are the Islamic Emirate of Afghanistan," he was quoted as saying.
A US State Department spokesperson had recently claimed "the Taliban and Haqqani network are separate entities", according to the report.
Mr Shaheen denied that the group had a role in the 1999 hijacking of an Indian plane to Afghanistan, the BBC reports.
The state-run Indian Airlines jet was hijacked en route to Delhi from Kathmandu with 180 people on board. It was flown to Kandahar, from where the hijackers negotiated the release of militants fighting in Kashmir, according to the report.
India released three Kashmiri militants in exchange for the passengers. None of the five armed hijackers was caught, according to the report.
He was quoted as saying it had extended all help, and that the Indian government should have been "thankful" to the group.
"India had requested us [for landing in Kandahar] because the jet had insufficient fuel, and then we helped in the release of the hostages," he was quoted as saying.
Mr Shaheen also denied knowledge of the circumstances under which the Indian photojournalist Danish Siddiqui was killed in Afghanistan in July, the BBC report notes.
The Pulitzer prize-winning Reuters journalist was embedded with a convoy of Afghan forces that was ambushed by the Taliban militants in a town Spin Boldak bordering Pakistan, according to the report.
He was quoted as saying he would share the details after the completion of the groups's investigation into the incident.