Speaking to CNBC's Hadley Gamble, Khan claimed India has been taken over by "extremist ideology" that could potentially spill over into armed conflict between the two nuclear rivals.
"Kashmir is, you know, it's a far more serious problem than people realize, (than) the world realizes. The problem is that India has been taken over by an extremist ideology, which is called Hindutva or the RSS," he said at the World Economic Forum in Davos, Switzerland.
Khan was referring to the Rashtriya Swayamsevak Sangh (RSS), a Hindu nationalist group affiliated with Indian Prime Minister Narendra Modi and his ruling Bharatiya Janata Party.
"This is serious because there are two nuclear-armed countries," Khan said. "That's why I want President Trump, head of the most powerful country in the world — he should intervene right now. United Nations, or President Trump through the U.N. at least."
India's Ministry of External Affairs responded to Khan's statements by calling them "factually inaccurate and contradictory."
Pakistan, the ministry said, should understand that "the global community has seen through this double-standard of playing the victim card in their fight against terror on the one hand, and supporting terror groups targeting India and other countries on the other."
"If Pakistan is indeed serious for a peaceful and normal relationship with India as (Khan) claims, the onus is on Pakistan to create a conducive atmosphere," the ministry said. "They have to take credible, irreversible and verifiable action against terror groups operating from its soil rather than making misleading and alarmist statements to divert the attention of international community."
Last year, fresh off a landslide re-election victory in Parliament, Modi's government revoked the state of Jammu & Kashmir's special status that allowed it to make its own laws. As a result, people from outside the state can potentially move in to settle there, buy land, and take government jobs or scholarships.
Anticipating backlash, India had deployed tens of thousands of troops across the Kashmir valley, banned public movements, shut down schools and colleges, cut off access to the internet and so on, affecting the lives of millions in the area.
Both countries lay claim to the Kashmir region in full but control only parts of it. They have fought multiple wars over the area, and the India-controlled region had been affected by an insurgency that started in the late 1980s.
Recently, India's Supreme Court ruled that an indefinite shutdown of the internet in Kashmir was illegal and rebuked the government for the communications lockdown, Reuters reported.
"Kashmir is a disputed territory between Pakistan and India," Khan said.
"The people of Kashmir, through a referendum could decide whichever country they wanted to join. Now, that disputed territory has been annexed by India, and, they are trying to change the demography of (the) people of Kashmir, which according to the fourth Geneva Convention is a war crime," he added.
While Pakistan has always called for international mediation in the Kashmir dispute, India has maintained it is a bilateral issue.
Khan also expressed concern about ongoing protests in India over a controversial citizenship bill passed last December that many say is set to disproportionately affect Muslims.
—CNBC's Ted Kemp and Naman Tandon contributed to this report.