The Indian government issued a stark rebuff on Tuesday by saying the US president's services were never requested, despite Trump saying they were.
Trump told reporters on Monday that Indian prime minister Narendra Modi had asked him, during a meeting at last month's G20 summit, if he would like to be a mediator on Kashmir, a territory at the centre of decades of sharp hostility between India and Pakistan.
His comments at the White House were welcomed by Pakistani prime minister Imran Khan, who hailed Trump's offer of involvement as raising the hopes of the millions who live in the tense region.
But across the border in India, reports that Modi had invited Trump to help calm the febrile climate in Kashmir sparked a political storm.
Opposition leaders accused Mr Modi of "betraying India's interests" and called for him to speak out decisively to reject Trump's remarks, but thus far he has remained silent.
The row could prove devastating for the Trump administration, as it risks further straining political ties with India which are already under pressure over trade.
Many Indians were left furious that their leader could part ties with the unwritten rule around the territory - that the involvement of foreign powers is not welcome.
Foreign Minister Subrahmanyan Jaishankar, who was part of the Indian delegation in Japan where Mr Trump and Mr Modi met, told agitated lawmakers that Modi did not seek any help from Trump over Kashmir.
"The U.S. president made certain remarks to the effect he was ready to mediate if requested by India and Pakistan. I categorically assure the house that no such request has been made by the prime minister, I repeat, no such request was made," he told parliament.
India, which has a Hindu majority, has long maintained the view that Kashmir, a Muslim-majority Himalayan region, is an integral part of its own country.
But Islamic Pakistan makes the same claim, hence the land has become some of the most contested in recent history, a war of words and weapons that has seen the nuclear-armed neighbours go to war twice since independence in 1947.
Pakistan has long pressed for the implementation of decades-old UN resolutions calling for a ballot for the region to decide its future, but India says the United Nations has no role in Kashmir, where separatist militants have been battling Indian forces for years.
Tension between the two countries has been high since an attack on an Indian military convoy in Kashmir in February, claimed by a Pakistani militant group, prompted India to send warplanes into Pakistan.
Pakistan retaliated by ordering its jets into India's side of Kashmir the following day, raising the prospect of a wider conflict that would only raise a death toll already in the tens of thousands.
It is a situation that the international community is keen to avoid given the severe geopolitical ramifications of a escalation in tensions.
The United States is invested in winning Pakistan's cooperation, seeing it as crucial to any deal to ensure the country does not become a base for militant groups like Islamic State after their fall from prominence in Afghanistan and Iraq.
But Mr Jaishankar closed any possibility of Trump joining the affray, saying there could strictly be no third-party involvement in India's problems with Pakistan.
"I also reiterate that it has been India's position that all outstanding issues are discussed only bilaterally," he said.
"I further underline any engagement with Pakistan would require an end to cross-border terrorism."
Pakistan denies Indian accusations that it gives material help to the militants fighting Indian rule in Kashmir for nearly three decades, but says it gives moral and diplomatic support to the Kashmiri people in their struggle for self-determination.
It is not the first embarrassment for Trump after his remarks at the summit in Japan, as the U.S. State Department took to twitter soon after, adamant that resolving the issue of Kashmir was a matter for the two countries themselves.
US officials said: "While Kashmir is a bilateral issue for both parties to discuss, the Trump administration welcomes Pakistan and India sitting down and the United States stands ready to assist."
The Democratic chairman of the US House of Representatives Foreign Affairs Committee, Eliot Engel, spoke to the Indian ambassador to reassure him there was no change in the U.S. position on Kashmir, the committee said on Twitter.
"Engel reiterated his support for the longstanding U.S. position on the Kashmir dispute, saying he supported dialogue between India & Pakistan, but the dialogue's space and scope can only be determined by India & Pakistan," the post read.
He added that Pakistan must "dismantle the terrorist infrastructure" for any meaningful dialogue with India.
India accuses Pakistan of arming and training insurgents who have been fighting since 1989 for Kashmir's independence from India or its merger with Pakistan, a charge that Islamabad denies.
The two sides cut dialogue on outstanding issues after Mr Modi's government came to power in 2014, with India demanding that Pakistan first end cross-border terrorism.
Agencies contributed to this report
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