Addressing the media ahead of their 45-minute bilateral on the sidelines of the G7, Modi conveyed clearly that issues between India and Pakistan are bilateral in nature and there was no need for third party mediation, as both countries were capable of solving their problems together.
To a question on Kashmir, Trump said: "Well, 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 also made clear that "all issues between India and Pakistan are bilateral, and we can find solutions between ourselves through dialogue".
Ahead of their meeting, Trump had said on August 21 that he would discuss the Kashmir issue with "friend" Modi in Biarritz and do his best to mediate in the issue.
Trump had told reporters in the White House: "Kashmir is a very complicated place. You have the Hindus, and you have the Muslims, and I wouldn't say they get along so great. And that's what you have right now."
"And you have millions of people who want to be ruled by others, and maybe on both sides, and you have two countries that haven't gotten along in a long time.
"And frankly it's a very explosive situation. I spoke to Prime Minister Khan, and yesterday I spoke to PM Modi; and they are both friends of mine, and they are great people, they're great people. And they love their countries, and they are in a very tough situation.
"Kashmir is a very tough situation, and this has been going on for decades, and decades; shooting, and I don't mean shooting like shooting a rifle, but major shooting of howitzers, of heavy arms, and this has been going on for a long, long period of time.
"But I get along really well with both of them. As you know, Prime Minister Khan was here just recently.
"And I'm going to meet Prime Minister Modi, I will be with PM Modi over the weekend, in France.
"And I think we're helping the situation, but there's tremendous problems between the two countries. And I will do the best I can to mediate or do something," he said.
Trump had last week phoned up both Modi and Imran 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 )