When the two leaders spoke to the media ahead of their 45-minute bilateral on the sidelines of the G7, Modi firmly reiterated that Kashmir was a bilateral issue, ruling out mediation by the US President.
"All the issues are of bilateral nature," Modi said when asked if he wanted mediation in the matter.
Trump, when asked if his offer to mediate was still on the table, said: "I'm here," but added that he thinks India and Pakistan can do it on their own.
Their declarations set at rest the confusion caused by Trump's off-the-cuff claim that Modi had asked him to mediate on Kashmir when they last met in Osaka in June during the G20 meeting.
Trump said: "We spoke last night about Kashmir, and Prime Minister Modi feels that he has it under control; and now when they speak with Pakistan I'm sure they will be able to do something. They will be able to do something probably very good."
Modi, asked a question on Kashmir, said: "India and Pakistan have several bilateral issues. And after the election of Prime Minister Imran Khan, I told him that both our countries have to fight against poverty, illiteracy, backwardness and both should work for the betterment of our people.
"And I have conveyed this to President Trump as well, and we keep discussing our bilateral issues," he added.
Modi spoke in Hindi and an interpreter translated his remarks. Trump, who has an antagonistic relationship with the media, quipped: "He actually speaks great English, he just doesn't want to talk to you."
The Indian Prime Minister laughed out loud and the two leaders clasped hands.
"It's great to be here with Prime Minister Modi," Trump said, adding that they "would discuss trade and the military at their bilateral meeting.
Modi called Trump a "friend" and said it was a "very important meeting for me".
The US and India "shared democratic values", said the Indian leader as he thanked Trump for congratulating him after his recent election.
Trump said he "learned a lot about India" from Modi at dinner Sunday night and that it is a "fascinating place, it's a beautiful place".
While preparing for a meeting with Pakistan's Prime Minister Imran Khan at the White House in July, Trump had sown confusion the claim that Modi had asked him to mediate on Kashmir.
India resolutely denied the claim, pointing out that ever since the signing of the Simla Agreement between the leaders of the two countries in 1971, disputes with Pakistan were bilateral matters without room for third party intervention.
Ahead of the Modi-Trump meeting, a senior US official tried to lay the issue to rest by stating categorically: "We just note that India has not requested any formal mediation."
Trump had last week phoned up both Modi and Khan on the Kashmir issue, after Pakistan went on the offensive over India ending the special status of Kashmir and bifurcating the state into two Union Territories - J&K and Ladakh.
During the call, Modi had 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's anti-India venom over the Kashmir issue.
The US has reaffirmed that there was no change in its Kashmir policy that it is a bilateral issue between India and Pakistan.
( With inputs from IANS )