image sourceAFPimage captionSuhail Shaheen also said the Taliban had "no policy" of launching armed operations against any country.
The Taliban intends to "raise its voice for Muslims" in Indian-administered Kashmir, a spokesman told the BBC.
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.
There has been violence on the Indian-run side for 30 years, because of a separatist insurgency.
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.
This is the first time the group has commented on Indian-administered Kashmir.
In an recent interview with CNN-News18 Taliban leader Anas Haqqani 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.
- What happened with Kashmir and why it matters
Mr Shaheen 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.
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.
image sourceGetty Imagesimage captionIndia has had a fraught relationship with Kashmir for decades
With Taliban in control of Afghanistan, many in India fear that sections within the group could now set their eyes Indian-administered Jammu and Kashmir, egged on by anti-India elements within Pakistan.
In a widely circulated TV debate clip, Pakistan's ruling PTI leader Neelam Irshad Sheikh said: "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.
- Why more locals in Kashmir are becoming militants
The Haqqani group has engineered and carried out attacks in the past against Indian assets, including the Indian embassy in Kabul, according to Carnegie India report on India's Afghanistan strategy following the US withdrawal.
Mr Shaheen claimed the allegations against the Haqqanis are mere claims.
"The Haqqanis are not a group. They are part of the Islamic Emirate of Afghanistan. They are the Islamic Emirate of Afghanistan," he said.
A US State Department spokesperson had recently claimed "the Taliban and Haqqani network are separate entities".
image sourceAFPimage captionTaliban fighters near the Indian Airlines plane which was hijacked to Kandahar in December 1999
Mr Shaheen denied that the group had a role in the 1999 hijacking of an Indian plane to Afghanistan.
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.
India released three Kashmiri militants in exchange for the passengers. None of the five armed hijackers was caught.
He said 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 said.
Mr Shaheen also denied knowledge of the circumstances under which the Indian photojournalist Danish Siddiqui was killed in Afghanistan in July.
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.
He said he would share the details after the completion of the groups's investigation into the incident.