"He (PM Modi) actually speaks very good English, he just doesn't want to talk," Trump joked when Prime Minister Modi asked reporters to let the leaders talk in privacy.
The two leaders also held each other's hand while everybody present in the room burst into laughter.
Modi called Trump a "friend" and said it was a "very important meeting for me".
He thanked the US president for congratulating him after his recent election victory and said their two countries had "shared democratic values".
"It's great to be here with Prime Minister Modi," Trump said, adding that he "learned a lot about India" from Modi at the G7 Summit dinner on Sunday.
"Fascinating place. It's a beautiful place," Trump said.