In a tweet on Monday, Trump said though Kashmir was a "tough situation", he had "good conversations" with both the leaders.

"Spoke to my two good friends, Prime Minister Modi of India, and Prime Minister Khan of Pakistan, regarding trade, strategic partnerships and, most importantly, for India and Pakistan to work towards reducing tensions in Kashmir. A tough situation, but good conversations," he tweeted.

Trump first called up Modi earlier on Monday during which they held a 30-minute talk.

Modi conveyed that "extreme rhetoric and incitement to anti-India violence by certain leaders in the region was not conducive to peace", in a reference to the Pakistani leadership spewing anti-India venom over the Kashmir issue.

Prime Minister Khan has been regularly taking to Twitter to attack Modi, calling him a fascist and racist. He has also alleged that Modi was turning India into a Hindu supremacist country, and that Muslims in the country were being disenfranchised and "RSS goons were on the rampage".

During the call, the Indian leader also highlighted the importance of creating an environment free from terror and violence and eschewing cross-border terrorism without exception, the Indian Ministry of External Affairs (MEA) said in a statment.

Modi reiterated India's commitment to cooperate with anyone who followed this path, in fighting poverty, illiteracy and disease.

The conversation comes days after the UN Security Council backed India in its efforts to bring in development in Kashmir after revoking its special status.

According to a White House readout of the conversation, Trump spoke with Modi to discuss regional developments and the US-India strategic partnership. The President also conveyed the importance of reducing tensions between India and Pakistan and maintaining peace in the region.

The two leaders further discussed strengthening of US-India economic ties through increased trade, and looked forward to meeting again soon, the readout added.

Later, Trump called up Khan.

Pakistan Foreign Minister Shah Mehmood Qureshi on Monday night said Trump made a call to Khan after his talk with Modi on the prevailing situation in Kashmir.

In a press briefing in Islamabad on Monday, Qureshi said that in response to Khan's call on August 16, Trump made a call to Narendra Modi and "expressed the desire in lowering tensions between Pakistan and India", Radio Pakistan reported.

A White House readout of the talk said: "President Trump spoke by telephone with Khan to discuss the need to reduce tensions and moderate rhetoric with India over the situation in Jammu and Kashmir.

"Trump reaffirmed the need to avoid escalation of the situation, and urged restraint on both sides. The two leaders also agreed to work together to strengthen US-Pakistan economic and trade cooperation."

In his August 16 phone call to Trump, Khan had voiced his concerns over India's "illegal" move in Kashmir, ahead of the UNSC closed-door discussion on Kashmir.

Khan told Trump that New Delhi's moves on Kashmir posed a threat to regional peace. Trump conveyed to Khan the importance of India and Pakistan reducing tension through bilateral dialogue.

The talks between Trump and Modi came days after US Deputy Secretary of State John Sullivan held talks with Indian External Affairs Minister S. Jaishankar in New Delhi to take forward the "deep convergences" in the India-US strategic ties, with both sides focussing on a rules-based order in the Indo-Pacific, where China has increased its footprint.

The US has reaffirmed that there was no change in its Kashmir policy, that it is a bilateral issue between India and Pakistan.

The Modi-Trump phone call was marked by the warmth and cordiality which characterises the relations between the two leaders, the MEA statement said.

The Prime Minister recalled their meeting in Japan's Osaka on the sidelines of the G-20 summit in June.

Referring to their bilateral discussions in Osaka, he expressed hope that the Commerce Minister of India and the US Trade Representative would meet at an early date to discuss bilateral trade prospects for mutual benefit.

Recalling that Monday marked 100 years of the Independence of Afghanistan, he reiterated India's longstanding and unwavering commitment to work for a united, secure, democratic and truly independent Afghanistan, the statement said.

Modi also said that he appreciated remaining in regular touch with the US President.

The Modi-Trump conversation in Osaka had been the subject of much speculation last month after Trump told Khan in Washington on July 22 that the Indian Prime Minister had asked him to mediate in the Kashmir issue.

But India strongly denied the statement, while Pakistan warmly welcomed it. The US immediately clarified Washington's stand on the Kashmir issue, saying that it was a bilateral issue between New Delhi and Islamabad.