Mr Obama, himself a 2009 peace prize winner, met Mr Satyarthi for a few minutes on the sidelines of a town hall event on the third and final day of his India visit.
The Indian child rights crusader told Mr Obama that winning the award has resulted in "tremendous moral pressure to work even harder than before".
He also lauded Obama administration's efforts to "bring down the number of child labourers."
"I made a plea to my fellow Nobel Laureate that we should forge a friendship to put an end to child slavery and labour to make the world a safer place for children and to bring children and youth into leadership roles in making a non-violent world," Mr Satyarthi said.
US First Lady Michelle Obama interacted with the children and told them that she would visit their shelter with her daughter if they come visiting India again.
"She told me that I have a daughter like you and next time if I come to India I will visit Bal Ashram with my daughter. She also asked me to keep up the good work," said one of the children, a young girl who was forced into a child marriage and later rescued by BBA.
According to BBA, which did not name the girl to protect her identity, she is now a 'Bal Sarpanch' at a Rajasthan village, who has helped rescue 46 child labourers till date and is also actively campaigning against child marriage.