Speaking on Fox News Special Report, Shringla said on Monday: "President Trump has made it very clear that his offer to mediate on Jammu and Kashmir is dependent on both India and Pakistan accepting it. Since India has not accepted the offer of mediation, President Trump has made it clear that this is not on the table any more. That has been the US' long-standing policy."
During Pakistan Prime Minister Imran Khan's visit to Washington, Trump had made the startling claim that Prime Minister Narendra Modi had asked him to mediate on Kashmir.
New Delhi quickly denied that any such request had been made, saying it was against its long-standing policy and that the agreements between India and Pakistan should be settled bilaterally.
Acting Assistant Secretary of State for South and Central Asian Affairs, Alice G. Wells, later tweeted a clarification, saying: "While Kashmir is a bilateral issue for both parties to discuss, the Trump administration welcomes #Pakistan and #India sitting down and the US stands ready to assist."
After India scaled back Kashmir's special status under constitutional provisions of Articles 370 and 35A, State Department spokesperson Morgan Ortagus said that it was an "internal matter" of India.
Fox News Special Report is one of the most popular programmes with a viewership of about 2.75 million and is hosted by the network's Chief Political Anchor Bret Baier.
During the interview, Shringla asserted: "The UN Secretary-General (Antonio Guterres) was also very clear, he has said that this issue has to be settled bilaterally between India and Pakistan in keeping with the agreement that the two countries have signed the Simla Agreement and the Lahore Declaration. So this is not an issue to be settled with third parties."
"I think that was something President Trump clarified and made clear," he added.
Earlier in the programme, Pakistan's Ambassador Asad Majeed Khan made a plea for international intervention. He told Baier: "It is for the UN, it is for friends like the US and other international players may be to intervene. In fact, President Trump offered to mediate."
Shringla said the restrictions in Kashmir were temporary and meant to prevent terrorist infiltration and incitement when the announcement about the reorganization was made.
The situation was returning to normal in Kashmir and tens of thousands of people were celebrating Eid, even causing "traffic jams", he added.
He said that the steps India has taken were to bring development and good governance to Kashmir, which had been hampered by Article 370 of the Constitution.
In the last 15 years, $40 billion was allocated to Kashmir for development, but little of that reached the common people, he said.
Reacting to a tweet by Imran Khan likening the Bharatiya Janata Party to the Nazis, Shringla said that unlike Pakistan, India was a secular democracy with 200 million Muslims, the second largest population of the religion's adherents in the world.
Even what was a part of Pakistan, had broken away in 1971 to form Bangladesh as a secular democracy like India "where minorities live in harmony with the rest of the majority population, is not the case in Pakistan", he said.
Imran Khan does not have the right to speak for India's Muslims, he added.
"Because we are a democracy, because we give voice to all the people in the country irrespective of religion, there is very little off-take of Indian Muslims for the Islamic State or Al Qaeda unlike many other countries, including Pakistan," he said.
(Arul Louis can be reached at arul.l@.in and followed on Twitter @arulouis)
( With inputs from IANS )